diff --git a/problem_data/no079.txt b/problem_data/no079.txt
new file mode 100644
index 0000000..b6f9903
--- /dev/null
+++ b/problem_data/no079.txt
@@ -0,0 +1,50 @@
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diff --git a/problem_data/no081.txt b/problem_data/no081.txt
new file mode 100644
index 0000000..1e9e6cd
--- /dev/null
+++ b/problem_data/no081.txt
@@ -0,0 +1,80 @@
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diff --git a/problem_data/no082.txt b/problem_data/no082.txt
new file mode 100644
index 0000000..1e9e6cd
--- /dev/null
+++ b/problem_data/no082.txt
@@ -0,0 +1,80 @@
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diff --git a/problem_data/no083.txt b/problem_data/no083.txt
new file mode 100644
index 0000000..1e9e6cd
--- /dev/null
+++ b/problem_data/no083.txt
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diff --git a/problem_data/no098.txt b/problem_data/no098.txt
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+++ b/problem_data/no098.txt
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\ No newline at end of file
diff --git a/problem_data/no099.txt b/problem_data/no099.txt
new file mode 100644
index 0000000..92201db
--- /dev/null
+++ b/problem_data/no099.txt
@@ -0,0 +1,1000 @@
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\ No newline at end of file
diff --git a/problem_data/no107.txt b/problem_data/no107.txt
new file mode 100644
index 0000000..19d7ba3
--- /dev/null
+++ b/problem_data/no107.txt
@@ -0,0 +1,40 @@
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diff --git a/python_code/complete/no051.py b/python_code/complete/no051.py
new file mode 100644
index 0000000..989f2b9
--- /dev/null
+++ b/python_code/complete/no051.py
@@ -0,0 +1,31 @@
+from python_code.functions import sieve
+
+def max_digs(n):
+    digs = set(str(n))
+    counts = [(dig, str(n).count(dig)) for dig in digs]
+    return sorted(counts, key=lambda pair: pair[1])[-1]
+
+def find_and_replace(n, dig):
+    digits = range(10)
+    if str(n)[0] == dig:
+        digits.remove(0) # no leading 0s
+
+    string_val = str(n)
+    result = [string_val.replace(dig, str(substitute))
+              for substitute in digits]
+    return [int(xx) for xx in result]
+
+PRIMES = sieve(10**6)
+
+for prime in PRIMES:
+    digit, count = max_digs(prime)
+    if count > 2:
+        candidates = find_and_replace(prime, digit)
+        match_count = 0
+        for candidate in candidates:
+            if candidate in PRIMES:
+                match_count += 1
+        if match_count == 8:
+            winner = prime
+            break
+print winner
diff --git a/python_code/complete/no060.py b/python_code/complete/no060.py
new file mode 100644
index 0000000..3b16d50
--- /dev/null
+++ b/python_code/complete/no060.py
@@ -0,0 +1,46 @@
+import operator
+
+from python_code.functions import is_prime
+from python_code.functions import sieve
+
+MAX_n = 10**4
+PRIMES = sieve(MAX_n)
+num_primes = len(PRIMES)
+partner_hash = {}
+for first in range(num_primes - 1):
+    prime1 = PRIMES[first]
+    for second in range(first + 1, num_primes):
+        prime2 = PRIMES[second]
+        cand1 = int(str(prime1) + str(prime2))
+        cand2 = int(str(prime2) + str(prime1))
+        if is_prime(cand1, primes=PRIMES, failure_point=MAX_n**2):
+            if is_prime(cand2, primes=PRIMES, failure_point=MAX_n**2):
+                if prime1 in partner_hash:
+                    partner_hash[prime1].append(prime2)
+                else:
+                    partner_hash[prime1] = [prime2]
+                if prime2 in partner_hash:
+                    partner_hash[prime2].append(prime1)
+                else:
+                    partner_hash[prime2] = [prime1]
+
+size = 1
+valid = [[prime] for prime in partner_hash]
+for size in range(2, 5 + 1):
+    next = []
+    for subset in valid:
+        could_add = partner_hash[subset[0]]
+        for prime in subset:
+            could_add = [p for p in could_add
+                         if p in partner_hash[prime]]
+        next.extend([subset[:] + [cand] for cand in could_add])
+    valid = next
+
+min_sum = 10**10
+min_set = None
+for subset in valid:
+    if sum(subset) < min_sum:
+        min_sum = sum(subset)
+        min_set = subset
+
+print min_sum, min_set
diff --git a/python_code/complete/no073 b/python_code/complete/no073
new file mode 100755
index 0000000..3264c91
--- /dev/null
+++ b/python_code/complete/no073
@@ -0,0 +1,44 @@
+#!/usr/bin/env python
+
+# Consider the fraction, n/d, where n and d are positive integers.
+# If n < d and HCF(n,d)=1, it is called a reduced proper fraction.
+
+# If we list the set of reduced proper fractions for d <= 8 in
+# ascending order of size, we get:
+# 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2,
+# 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
+
+# It can be seen that there are 3 fractions between 1/3 and 1/2.
+
+# How many fractions lie between 1/3 and 1/2 in the sorted set of
+# reduced proper fractions for d <= 12,000?
+
+# ALGO
+# We simply seek 1/3 <= n/d <= 1/2 with (n, d) = 1
+# This is equivalent to d/3 <= n <= d/2 or
+# ceil(d/3) <= n <= floor(d/2)
+# Note we'll never have conflicts since for d > 3,
+# (n, d) = 1 implies n/d = 1/2 or n/d = 1/3 is
+# impossible
+
+from fractions import gcd
+from math import ceil
+from math import floor
+
+from python_code.decorators import euler_timer
+
+@euler_timer(73)
+def main():
+    MAX_d = 12000
+
+    count = 0
+    for d in range(4, MAX_d + 1):
+        low = int(ceil(d/3.0))
+        high = int(floor(d/2.0))
+        for n in range(low, high + 1):
+            if gcd(d, n) == 1:
+                count += 1
+    print count
+
+if __name__ == "__main__":
+    main()
diff --git a/python_code/complete/no077 b/python_code/complete/no077
new file mode 100755
index 0000000..532f408
--- /dev/null
+++ b/python_code/complete/no077
@@ -0,0 +1,103 @@
+#!/usr/bin/env python
+
+# It is possible to write ten as the sum of primes in
+# exactly five different ways:
+
+# 7 + 3
+# 5 + 5
+# 5 + 3 + 2
+# 3 + 3 + 2 + 2
+# 2 + 2 + 2 + 2 + 2
+
+# What is the first value which can be written as the sum of
+# primes in over five thousand different ways?
+
+#################################
+# Let pp(k, n) represent the number of partitions of n
+# using only primes at least as large as p_k (the kth prime)
+
+# Since the primes are either all greater than p_k or one
+# of them is equal we have
+# pp(k, n) = pp(k+1, n) + pp(k, n - p_k)
+# p_0 = 2, we want to compute pp(0, n) for all n and continue
+# doing so until pp(0, n) > 5000
+
+# Boundary
+# p(k, n) = 0 if p_k > n
+# p(k, n) = 1 if p_k = n
+# pp(k, n) = pp(k+1, n) + pp(k, n - p_k)
+
+############## EXAMPLE TABLE ##############
+# n\k | 0 | 1 | 2 |
+# -----------------
+#  1  | 0 | 0 | 0 |
+# -----------------
+#  2  | 1 | 0 | 0 |
+# -----------------
+#  3  | 1 | 1 | 0 |
+# -----------------
+#  4  | 1 | 0 | 0 |
+# -----------------
+#  5  | 1 | 1 | 1 |
+# -----------------
+
+from python_code.decorators import euler_timer
+from python_code.functions import sieve
+
+def prime_partitions(n, primes):
+    p = {}
+    for k in range(1, n + 1):
+        p[(k, k)] = 1
+        for i in range(k - 1, 0, -1):
+            if i > k - i:
+                p[(i, k)] = p[(i + 1, k)]
+            else:
+                p[(i, k)] = p[(i + 1, k)] + p[(i, k - i)]
+    return p[(1, n)]
+
+@euler_timer(77)
+def main():
+    max_prime_val = 10**2
+    PRIMES = sieve(max_prime_val)
+
+    pp = {(0, 1): 0,
+          (1, 1): 0,
+          (2, 1): 0,
+          (0, 2): 1,
+          (1, 2): 0,
+          (2, 2): 0}
+    curr_val = -1
+    n = 2
+    curr_prime_index = 1
+    while curr_val < 5000:
+        n += 1
+        if n > PRIMES[curr_prime_index]:
+            curr_prime_index += 1
+            if curr_prime_index >= len(PRIMES):
+                raise ValueError("Primes is too small: %s" % curr_val)
+
+        prime_index = curr_prime_index
+        # First reduce the prime_index, "k" until the prime itself
+        # does not exceed n
+        while PRIMES[prime_index] > n:
+            pp[(prime_index, n)] = 0
+            prime_index -= 1
+        # If n is a prime number, then after doing so, we know that
+        # PRIMES[prime_index] == n, hence pp(p_i, n) = 1 and we
+        # can reduce the index further
+        if PRIMES[prime_index] == n:
+            pp[(prime_index, n)] = 1
+            prime_index -= 1
+
+        for index in range(prime_index, -1, -1):
+            prime_val = PRIMES[index]
+            if prime_val > n - prime_val:
+                pp[(index, n)] = pp[(index + 1, n)]
+            else:
+                pp[(index, n)] = pp[(index + 1, n)] + pp[(index, n - prime_val)]
+
+        curr_val = pp[(0, n)]
+    print n
+
+if __name__ == "__main__":
+    main()
diff --git a/python_code/complete/no078.py b/python_code/complete/no078.py
new file mode 100644
index 0000000..30cc536
--- /dev/null
+++ b/python_code/complete/no078.py
@@ -0,0 +1,27 @@
+from python_code.functions import polygonal_number
+
+def find_residue(residue):
+    p = {0: 1}
+
+    pentagonal = []
+    pent_index = 1
+    while True:
+        if pent_index > 0:
+            next_index = -pent_index
+        else:
+            next_index = -pent_index + 1
+        begin = polygonal_number(5, pent_index)
+        end = polygonal_number(5, next_index)
+        pentagonal.append(begin)
+        for n in range(begin, end):
+            p[n] = 0
+            for index, val in enumerate(pentagonal):
+                if (index/2) % 2 == 0:
+                    p[n] = (p[n] + p[n - val]) % residue
+                else:
+                    p[n] = (p[n] - p[n - val]) % residue
+            if p[n] == 0:
+                return n
+        pent_index = next_index
+
+print find_residue(10**6)
diff --git a/python_code/complete/no079.py b/python_code/complete/no079.py
new file mode 100644
index 0000000..d186620
--- /dev/null
+++ b/python_code/complete/no079.py
@@ -0,0 +1,27 @@
+from python_code.functions import get_data
+
+data = [[int(dig) for dig in row] for row
+        in get_data(79).split("\r\n") if row]
+
+matches = {}
+for attempt in data:
+    a, b, c = attempt
+    keys = [((a, b), (c, 'Right')),
+            ((a, c), (b, 'Middle')),
+            ((b, c), (a, 'Left'))]
+    for key, val in keys:
+        if key in matches:
+            matches[key].append(val)
+        else:
+            matches[key] = [val]
+
+for val in matches.values():
+    val.sort()
+
+# 73162890
+# no (7, a) have left values so we choose 7 as the leftmost
+# The majority of (b, a) with no left value are in 7 and 3
+# so we start 73. Using the pairs with 7 and 3 first,
+# and no left values we can put together the solution
+# and verify it gels with all the conditions
+print 73162890
diff --git a/python_code/complete/no080 b/python_code/complete/no080
new file mode 100755
index 0000000..84a424c
--- /dev/null
+++ b/python_code/complete/no080
@@ -0,0 +1,91 @@
+#!/usr/bin/env python
+
+# It is well known that if the square root of a natural number is not an
+# integer, then it is irrational. The decimal expansion of such square
+# roots is infinite without any repeating pattern at all.
+
+# The square root of two is 1.41421356237309504880..., and the digital
+# sum of the first one hundred decimal digits is 475.
+
+# For the first one hundred natural numbers, find the total of the digital sums
+# of the first one hundred decimal digits for all the irrational square roots.
+
+###########################
+# To deal with precision, we use no064 and no065 to help out.
+# The expanded_digits function will expanded n/d to d digits no matter
+# the precision simply by multiplying by 10
+
+# We use the cycle (algorithm calculated in 64) to find the values of a_i
+# in the continued fraction expansion and we use the recurrence on
+# the numerator and denominator in the fractional estimate as in
+# 65. Once these estimates agree to 100 digits, we stop
+
+from math import sqrt
+from fractions import gcd
+
+from python_code.decorators import euler_timer
+from python_code.functions import recurrence_next
+
+def expanded_digits(numerator, denominator, digits):
+    # use integer division on num and denom to get a quotient
+    quotient_digits = [int(dig) for dig in str(numerator/denominator)]
+    remainder = numerator % denominator
+    if len(quotient_digits) >= digits:
+        return quotient_digits[:digits]
+    return quotient_digits + expanded_digits(10*remainder,
+                                             denominator,
+                                             digits - len(quotient_digits))
+
+def next(current, n):
+    A, B, C = current
+    a = int(C*(1.0)/(A*sqrt(n) + B))
+    r = (C*A, -C*B - a*(n*A**2 - B**2), n*A**2 - B**2)
+    d = gcd(gcd(r[0], r[1]), r[2])
+    return ( r[0]/d, r[1]/d, r[2]/d )
+
+def cycle(n):
+    result = [int(sqrt(n))]
+    init = curr_r = (1, -int(sqrt(n)), 1)
+
+    result.append(int(curr_r[2]*(1.0)/(curr_r[0]*sqrt(n) + curr_r[1])))
+    curr_r = next(curr_r, n)
+    while curr_r != init:
+        result.append(int(curr_r[2]*(1.0)/(curr_r[0]*sqrt(n) + curr_r[1])))
+        curr_r = next(curr_r, n)
+    return result
+
+def stable_expansion(digits, n):
+    values = cycle(n)
+    h_values = [1, values[0]] # a_0
+    k_values = [0, 1]
+
+    cycle_length = len(values) - 1 # we only cycle over a_1,...,a_{k-1}
+    last = expanded_digits(h_values[1], k_values[1], digits)
+    index = 1
+    relation = [1, values[index]]
+    h_values = recurrence_next(relation, h_values)
+    k_values = recurrence_next(relation, k_values)
+    current = expanded_digits(h_values[1], k_values[1], digits)
+    while current != last:
+        index += 1
+        last = current
+
+        relative_index = ((index - 1) % cycle_length) + 1
+        # we want residues 1,..,k-1 instead of the traditional 0,...,k-2
+        relation = [1, values[relative_index]]
+        h_values = recurrence_next(relation, h_values)
+        k_values = recurrence_next(relation, k_values)
+        current = expanded_digits(h_values[1], k_values[1], digits)
+    return current
+
+@euler_timer(80)
+def main():
+    non_squares = [ num for num in range(1, 100 + 1)
+                    if int(sqrt(num))**2 != num ]
+    running_sum = 0
+    for n in non_squares:
+        running_sum += sum(stable_expansion(100, n))
+    print running_sum
+
+if __name__ == "__main__":
+    main()
diff --git a/python_code/complete/no081.py b/python_code/complete/no081.py
new file mode 100644
index 0000000..717185f
--- /dev/null
+++ b/python_code/complete/no081.py
@@ -0,0 +1,35 @@
+from python_code.functions import get_data
+
+def diamond_matrix(data):
+    result = {}
+    max_index = len(data) - 1
+    max_depth = 2*max_index
+    result[(max_index, max_index)] = data[-1][-1]
+
+    for depth in range(max_depth - 1, -1, -1):
+        initial = 0
+        final = depth
+        if depth > max_index:
+            initial = depth - max_index
+            final = max_index
+        for row in range(initial, final + 1):
+            column = depth - row
+            choices = []
+            if (row + 1, column) in result:
+                choices.append(result[(row + 1, column)])
+            if (row, column + 1) in result:
+                choices.append(result[(row, column + 1)])
+            result[(row, column)] = data[row][column] + min(choices)
+    return result[(0, 0)]
+
+# EXAMPLE = [[131, 673, 234, 103,  18],
+#            [201,  96, 342, 965, 150],
+#            [630, 803, 746, 422, 111],
+#            [537, 699, 497, 121, 956],
+#            [805, 732, 524,  37, 331]]
+# print diamond_matrix(EXAMPLE) == 2427
+
+data = [[int(entry) for entry in row.split(",")]
+        for row in get_data(81).split("\n") if row]
+
+print diamond_matrix(data)
diff --git a/python_code/complete/no082.py b/python_code/complete/no082.py
new file mode 100644
index 0000000..28484b8
--- /dev/null
+++ b/python_code/complete/no082.py
@@ -0,0 +1,28 @@
+from python_code.functions import get_data
+
+def column_by_column(data):
+    result = {}
+    size = len(data)
+    # First column is set
+    for row in range(size):
+        result[(row, 0)] = data[row][0]
+
+    for column in range(1, size):
+        for row in range(size):
+            set_val = result[(row, column - 1)] + data[row][column]
+            for under in range(row):
+                val = result[(under, column - 1)] + sum([data[ind][column] for ind in range(under, row + 1)])
+                if val < set_val:
+                    set_val = val
+            for over in range(row + 1, size):
+                val = result[(over, column - 1)] + sum([data[ind][column] for ind in range(row, over + 1)])
+                if val < set_val:
+                    set_val = val
+            result[(row, column)] = set_val
+
+    return min([result[(row, size - 1)] for row in range(size)])
+
+data = [[int(entry) for entry in row.split(",")]
+        for row in get_data(82).split("\n") if row]
+
+print column_by_column(data)
diff --git a/python_code/complete/no083.py b/python_code/complete/no083.py
new file mode 100644
index 0000000..93ef8ae
--- /dev/null
+++ b/python_code/complete/no083.py
@@ -0,0 +1,55 @@
+from python_code.functions import get_data
+
+def astar(graph, size, minimum):
+    start = (0, 0)
+    target = (size - 1, size - 1)
+    closed_nodes = {(0, 0): (None, graph[(0, 0)])}
+    # node, parent, distance, don't store heuristic dist.
+    open_nodes = {(1, 0): ((0, 0), graph[(0, 0)] + graph[(1, 0)]),
+                  (0, 1): ((0, 0), graph[(0, 0)] + graph[(0, 1)])}
+    def heuristic(node):
+        return (2*size - 2 - sum(node))*minimum
+
+    while target not in closed_nodes:
+        min_val = None
+        min_f = -1
+        for node in open_nodes:
+            val = open_nodes[node][1] + heuristic(node)
+            if min_val is None:
+                min_val = val
+                min_f = node
+            else:
+                if val < min_val:
+                    min_val = val
+                    min_f = node
+
+        closed_nodes[min_f] = open_nodes.pop(min_f)
+
+        min_val = min_val - heuristic(min_f)
+        node_x, node_y = min_f
+        adjacent = [(node_x + 1, node_y), (node_x - 1, node_y),
+                    (node_x, node_y + 1), (node_x, node_y - 1)]
+        adjacent = [pair for pair in adjacent
+                    if pair not in closed_nodes and pair in graph]
+        for node in adjacent:
+            if node in open_nodes:
+                comp_val = open_nodes[node][1]
+                new_val = min_val + graph[node]
+                if new_val < comp_val:
+                    open_nodes[node] = (min_f, new_val)
+            else:
+                open_nodes[node] = (min_f, min_val + graph[node])
+
+    return closed_nodes[target][1]
+
+data = [[int(entry) for entry in row.split(",")]
+        for row in get_data(83).split("\n") if row]
+
+arranged_data = {}
+size = len(data)
+for i in range(size):
+    for j in range(size):
+        arranged_data[(i, j)] = data[i][j]
+
+minimum = min(arranged_data.values())
+print astar(arranged_data, size, minimum)
diff --git a/python_code/complete/no086.py b/python_code/complete/no086.py
new file mode 100644
index 0000000..7ac0588
--- /dev/null
+++ b/python_code/complete/no086.py
@@ -0,0 +1,58 @@
+from math import sqrt
+
+def ascending(num, num_sum, min_num, prob_max):
+    if num_sum < min_num:
+        return []
+    if num == 1:
+        if num_sum == min_num:
+            return [[num_sum]]
+        else:
+            return []
+
+    next_sum = num_sum - min_num
+    biggest = next_sum/(num - 1) # integer division intended
+    biggest = min(biggest, prob_max)
+    result = []
+    for next_min in range(min_num, biggest + 1):
+        result.extend([[min_num] + cand for cand in
+                        ascending(num - 1, next_sum, next_min, prob_max)])
+    return result
+
+def short_distance_int(a, b, c):
+    best = min(sqrt(a**2 + (b + c)**2),
+               sqrt(b**2 + (c + a)**2),
+               sqrt(c**2 + (a + b)**2))
+    return int(best) == best
+
+def num_solutions(M, hash_):
+    if M in hash_:
+        return hash_[M]
+    if M == 0:
+        hash_[0] = 0
+        return 0
+
+    to_add = 0
+    for lowest in range(1, M):
+        # exactly 1 values M
+        for mid in range(lowest, M):
+            if short_distance_int(lowest, mid, M):
+                to_add += 1
+        # exactly 2 values M
+        if short_distance_int(lowest, M, M):
+            to_add += 1
+    # all values M
+    if short_distance_int(M, M, M):
+        to_add += 1
+    result = to_add + num_solutions(M - 1, hash_)
+    hash_[M] = result
+    return result
+
+TARGET = 10**6
+solution_hash = {0: 0}
+M = 1
+num_solutions(1, solution_hash)
+while solution_hash[M] <= TARGET:
+    M += 1
+    num_solutions(M, solution_hash)
+print M, solution_hash[M]
+# 1818
diff --git a/python_code/complete/no088.py b/python_code/complete/no088.py
new file mode 100644
index 0000000..848955a
--- /dev/null
+++ b/python_code/complete/no088.py
@@ -0,0 +1,34 @@
+from python_code.functions import all_factors
+
+MAX_n = 13000
+factor_hash = {1: [1]}
+factor_hash = all_factors(MAX_n, factor_hash)
+available = {}
+for i in range(1, MAX_n + 1):
+    available[i] = [factor for factor in factor_hash[i]
+                    if factor > 1 and factor**2 <= i]
+
+new_hash = {1: [[]], 2: [[2]]}
+value_hash = {}
+for i in range(3, 13000 + 1):
+    to_add = [[i]]
+    for factor in available[i]:
+        for subset1 in new_hash[factor]:
+            for subset2 in new_hash[i/factor]:
+                cand = sorted(subset1 + subset2)
+                if cand not in to_add:
+                    to_add.append(cand)
+    for match in to_add:
+        new_k = i + len(match) - sum(match)
+        if new_k > 1 and new_k not in value_hash:
+            value_hash[new_k] = i
+    new_hash[i] = to_add
+
+final_list = []
+for desired in range(2, 12001):
+    if desired not in value_hash:
+        raise Exception("Subset not large enough, raise MAX_n.")
+    if value_hash[desired] not in final_list:
+        final_list.append(value_hash[desired])
+
+print sum(final_list)
diff --git a/python_code/complete/no090.py b/python_code/complete/no090.py
new file mode 100644
index 0000000..7463755
--- /dev/null
+++ b/python_code/complete/no090.py
@@ -0,0 +1,60 @@
+from python_code.functions import all_subsets
+# def all_subsets(list_, size):
+
+from math import factorial
+import operator
+
+def total_perms(o_list):
+    counts = []
+    curr_entry = o_list[0]
+    curr_count = 1
+    for entry in o_list[1:]:
+        if entry == curr_entry:
+            curr_count += 1
+        else:
+            counts.append(curr_count)
+            curr_entry = entry
+            curr_count = 1
+    counts.append(curr_count)
+    return factorial(sum(counts))/reduce(operator.mul, [factorial(count) for count in counts])
+
+def ascending(num, num_sum, min_num, prob_max):
+    if num_sum < min_num:
+        return []
+    if num == 1:
+        if num_sum == min_num:
+            return [[num_sum]]
+        else:
+            return []
+
+    next_sum = num_sum - min_num
+    biggest = next_sum/(num - 1) # integer division intended
+    biggest = min(biggest, prob_max)
+    result = []
+    for next_min in range(min_num, biggest + 1):
+        result.extend([[min_num] + cand for cand in
+                        ascending(num - 1, next_sum, next_min, prob_max)])
+    return result
+
+def can_concat(left, right):
+    possible = ['%s%s' % (dig_l, dig_r) for dig_l in left for dig_r in right]
+    possible.extend(['%s%s' % (dig_l, dig_r) for dig_l in right for dig_r in left])
+    return (len(set(possible).intersection(
+        ['01', '04', '09', '16', '25', '36', '49', '64', '81'])) == 9)
+
+dice = all_subsets(range(10), 6)
+size = len(dice)
+for i in range(size):
+    if 6 in dice[i]:
+        if 9 not in dice[i]:
+            dice[i].append(9)
+    if 9 in dice[i]:
+        if 6 not in dice[i]:
+            dice[i].append(6)
+
+count = 0
+for left_ind in range(size - 1):
+    for right_ind in range(left_ind, size):
+        if can_concat(dice[left_ind], dice[right_ind]):
+            count += 1
+print count
diff --git a/python_code/complete/no093.py b/python_code/complete/no093.py
new file mode 100644
index 0000000..dcfc787
--- /dev/null
+++ b/python_code/complete/no093.py
@@ -0,0 +1,123 @@
+import operator
+
+from python_code.functions import all_permutations
+from python_code.functions import all_subsets
+
+# a D b D c D d, D in {+,-,*,/}
+# = {operator.add, operator.sub, operator.mul, operator.div}
+# (a b) c d
+# a b (c d)
+# (a b) (c d)
+# (a b c) d
+# ((a b) c) d
+# (a (b c)) d
+# a (b c d)
+# a ((b c) d)
+# a (b (c d))
+
+def do_operations_no_paren(operators, numbers):
+    if len(operators) + 1 != len(numbers):
+        raise Exception("MISDEED")
+
+    if len(numbers) == 1:
+        return numbers[0]
+
+
+    for i, op in enumerate(operators):
+        if op in [operator.mul, operator.div]:
+            new_number = op(numbers[i], numbers[i+1])
+            new_numbers = numbers[:i] + [new_number] + numbers[i+2:]
+            new_operators = operators[:i] + operators[i+1:]
+            return do_operations_no_paren(new_operators, new_numbers)
+
+    # no mul or div found
+    new_number = op(numbers[0], numbers[1])
+    new_numbers = [new_number] + numbers[2:]
+    new_operators = operators[1:]
+    return do_operations_no_paren(new_operators, new_numbers)
+
+def results(signs, numbers):
+    # parentheses first
+    # multiply or divide before add or subtract
+    # left to right after all
+    a, b, c, d = numbers
+    s1, s2, s3 = signs
+
+    result = []
+    try:
+        val = do_operations_no_paren([s2, s3], [s1(a, b), c, d])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s1, s2], [a, b, s3(c, d)])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s2], [s1(a, b), s3(c, d)])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s3], [do_operations_no_paren([s1, s2], [a, b, c]), d])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s3], [s2(s1(a, b), c), d])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s3], [s1(a, s2(b, c)), d])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s1], [a, do_operations_no_paren([s2, s3], [b, c, d])])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s1], [a, s3(s2(b, c), d)])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+    try:
+        val = do_operations_no_paren([s1], [a, s2(b, s3(c, d))])
+        result.append(val)
+    except ZeroDivisionError:
+        pass
+
+    return [int(n) for n in result if int(n) == n]
+
+def most_consecutive(dig_cands, sign_cands):
+    all_encountered = []
+    for perm in all_permutations(dig_cands):
+        for sign_set in sign_cands:
+            for number in results(sign_set, perm):
+                if number > 0 and number not in all_encountered:
+                    all_encountered.append(number)
+    biggest = 1
+    while biggest + 1 in all_encountered:
+        biggest = biggest + 1
+    return biggest
+
+SIGNS = [operator.add, operator.sub, operator.mul, operator.div]
+SIGN_CANDS = []
+for sign1 in SIGNS:
+    for sign2 in SIGNS:
+        for sign3 in SIGNS:
+            SIGN_CANDS.append([sign1, sign2, sign3])
+special_range = [n*1.0 for n in range(1, 10)]
+DIG_CANDS = all_subsets(special_range, 4)
+
+max_tuple = None
+max_val = 0
+for dig_cand in DIG_CANDS:
+    length = most_consecutive(dig_cand, SIGN_CANDS)
+    if length > max_val:
+        max_val = length
+        max_tuple = dig_cand
+print ''.join([str(int(n)) for n in max_tuple])
diff --git a/python_code/complete/no095.py b/python_code/complete/no095.py
new file mode 100644
index 0000000..fc21f33
--- /dev/null
+++ b/python_code/complete/no095.py
@@ -0,0 +1,69 @@
+from python_code.decorators import euler_timer
+from python_code.functions import all_factors
+from python_code.functions import first_prime_divisor
+from python_code.functions import robust_divide
+from python_code.functions import sieve
+
+n = 10**6
+PRIMES = sieve(n)
+
+def sum_factors(n, hash_={}, primes=[]):
+    if n in hash_:
+        return hash_[n]
+    elif n == 1:
+        hash_[1] = 1
+        return 1
+    if primes == []:
+        primes = sieve(n)
+
+    prime, _  = first_prime_divisor(n, primes)
+    quotient, count = robust_divide(n, prime, include_count=True)
+    factor = (prime**(count + 1) - 1)/(prime - 1)
+    hash_[n] = factor*sum_factors(quotient, hash_=hash_, primes=primes)
+    return hash_[n]
+
+def amicable_cycle(n, cycle_hash, factor_sum_hash, primes, break_point):
+    if n in cycle_hash:
+        return cycle_hash[n][1]
+
+    cycle = [n]
+    next = sum_factors(n, factor_sum_hash, primes) - n
+    while (next not in cycle_hash and
+           next not in cycle and
+           next <= break_point):
+        cycle.append(next)
+        next = sum_factors(next, factor_sum_hash, primes) - next
+
+    if next > break_point:
+        set_val = [None]
+    elif next in cycle_hash:
+        set_val = cycle_hash[next][1]
+    elif next in cycle:
+        start = cycle.index(next)
+        set_val = cycle[start:]
+    else:
+        raise Exception("Shouldn't happen")
+    for val in cycle:
+        cycle_hash[val] = (factor_sum_hash[val] - val, set_val[:])
+    return cycle_hash[n][1]
+
+chains = {1: (0, [0]),
+          2: (1, [0]),
+          3: (1, [0])}
+
+h = {1: 1,
+     2: 3,
+     3: 4}
+
+for i in range(4, n + 1):
+    amicable_cycle(i, chains, h, PRIMES, 10**6 + 1)
+
+best_length = 0
+longest_chain = None
+for i in range(1, n + 1):
+    chain = chains[i][1]
+    if len(chain) > best_length:
+        best_length = len(chain)
+        longest_chain = chain[:]
+
+print min(longest_chain)
diff --git a/python_code/complete/no095_sieve.py b/python_code/complete/no095_sieve.py
new file mode 100644
index 0000000..766559d
--- /dev/null
+++ b/python_code/complete/no095_sieve.py
@@ -0,0 +1,51 @@
+def proper_divisor_sums(n):
+    result = [0]*(n + 1)
+    # loop over all possible divisors
+    for divisor in xrange(1, n + 1):
+        # loop over all numbers that
+        # i divides properly (we want
+        # the sum of proper divisors)
+        for parent in xrange(2*divisor, n + 1, divisor):
+            result[parent] += divisor
+    return result
+
+def amicable_cycle(n, cycle_hash, divisors, break_point):
+    if n in cycle_hash:
+        return cycle_hash[n][1]
+
+    cycle = [n]
+    next = divisors[n]
+    while (next not in cycle_hash and
+           next not in cycle and
+           next <= break_point):
+        cycle.append(next)
+        next = divisors[next]
+
+    if next > break_point:
+        set_val = [None]
+    elif next in cycle_hash:
+        set_val = cycle_hash[next][1]
+    elif next in cycle:
+        start = cycle.index(next)
+        set_val = cycle[start:]
+    else:
+        raise Exception("Shouldn't happen")
+    for val in cycle:
+        cycle_hash[val] = (divisors[val], set_val[:])
+    return cycle_hash[n][1]
+
+MAX_n = 10**6
+divisors = proper_divisor_sums(MAX_n)
+chains = {1: (0, [0]),
+          2: (1, [0]),
+          3: (1, [0])}
+
+best_length = 1
+longest_chain = [0]
+for i in range(4, MAX_n + 1):
+    chain = amicable_cycle(i, chains, divisors, 10**6)
+    if len(chain) > best_length:
+        best_length = len(chain)
+        longest_chain = chain[:]
+
+print min(longest_chain)
diff --git a/python_code/complete/no096.py b/python_code/complete/no096.py
new file mode 100644
index 0000000..3eefb3a
--- /dev/null
+++ b/python_code/complete/no096.py
@@ -0,0 +1,548 @@
+#############################
+########## Imports ##########
+#############################
+
+import operator
+from os.path import exists
+import time
+from python_code.functions import get_data
+
+#############################
+######### Constants #########
+#############################
+
+GRID_KEY = {1: 1,
+            2: 4,
+            3: 7,
+            4: 28,
+            5: 31,
+            6: 34,
+            7: 55,
+            8: 58,
+            9: 61}
+
+#############################
+########## Errors ###########
+#############################
+
+class Error(Exception):
+    pass
+
+
+class NonuniqueListForSubset(Error):
+    pass
+
+
+class NonsenseSudokuValue(Error):
+    pass
+
+
+class NonsenseIndex(Error):
+    pass
+
+
+class NonsenseGridIndex(Error):
+    pass
+
+
+class BadSudokuFileInput(Error):
+    pass
+
+
+class WronglySpecifiedNode(Error):
+    pass
+
+
+class WronglySpecifiedStructure(Error):
+    pass
+
+
+class WronglySpecifiedValueDeclaration(Error):
+    pass
+
+
+class TooManyOccurences(Error):
+    pass
+
+
+class CheckFoundNoImprovement(Error):
+    pass
+
+
+class NodelistMissingValue(Error):
+    pass
+
+#############################
+###### Helper Functions #####
+#############################
+
+def subset(list_, size):
+    if len(list_) != len(set(list_)):
+        raise NonuniqueListForSubset(list_)
+    if size == 1:
+        return [ [entry] for entry in list_ ]
+    result = []
+    for entry in list_:
+        candidates = list_[:] # copy, though not entirely deep
+        candidates.remove(entry)
+        for subset_ in subset(candidates, size - 1):
+            to_add = sorted(subset_ + [entry])
+            if to_add not in result:
+                result.append(to_add)
+    return [ entry for entry in result ]
+
+
+def get_indices(structure, index):
+    if structure not in ('row', 'column', 'subgrid'):
+        raise WronglySpecifiedStructure(structure)
+    elif index not in range(1, 10):
+        raise NonsenseGridIndex(index)
+
+    if structure == 'row':
+        return [ 9*(index - 1) + j + 1 for j in range(9) ]
+    elif structure == 'column':
+        return [ index + 9*j for j in range(9) ]
+    elif structure == 'subgrid':
+        return [ GRID_KEY[index] + i + 9*j
+                 for i in range(3) for j in range(3) ]
+
+
+def get_first_node(nodes, value):
+    for node in nodes:
+        if value in node.choices:
+            # returns the actual object, not a copy
+            return node
+    raise NodelistMissingValue(value)
+
+
+def copy_remove(list_, val):
+    # assume val occurs 0 or 1 times in list_
+    if list_.count(val) > 1:
+        raise TooManyOccurences("%s in %s" % (val, list_))
+
+    result = list_[:]
+    if val in result:
+        result.remove(val)
+    return result
+
+
+def all_possible(structure_choices):
+    if len(structure_choices) == 0:
+        return []
+    elif len(structure_choices) == 1:
+        return [ choices[:] for choices in structure_choices[:] ]
+    result = []
+    working_choices = [ choices[:] for choices in structure_choices[1:] ]
+    # if this entry is empty, result will be as well, which is fine
+    for val in structure_choices[0]:
+        curr = [ copy_remove(choices, val) for choices in working_choices ]
+        result.extend([ [val] + arr for arr in all_possible(curr) ])
+    return result
+
+
+def hypothetical_setval(structure, index, value):
+    """
+    Helper for check structure
+
+    Returns hypothetical arrangements for structure given the
+    node at index is set to value.
+    """
+    if type(structure) != list:
+        raise WronglySpecifiedStructure(
+            "Type is %s, rather than list" % type(structure))
+    # since only called by check_structure, structure is
+    # validated there
+    if index not in range(9):
+        # this is the index within the structure, which is handed
+        # to us as a list
+        raise NonsenseIndex(index)
+    working_structure = [ node.copy() for node in structure ]
+    for ind in range(9):
+        # checks if value is legitimate
+        if ind != index:
+            working_structure[ind].scratch_value(value)
+    working_structure[index].set_final(value)
+    return all_possible([ node.choices for node in working_structure ])
+
+
+def uniq(list_):
+    return sorted(list(set(list_)))
+
+
+def check_structure(structure):
+    # assumes the structure is cleaned
+    if len(structure) != 9:
+        WronglySpecifiedStructure("Structure of length %s." % len(structure))
+    remaining = [ node.choices for node in structure
+                  if len(node.choices) > 1 ]
+    if remaining == []:
+        return (False, 0)
+    values = uniq(reduce(operator.add, remaining))
+    for value in values:
+        for i in range(9):
+            if value in structure[i].choices:
+                # may need to actually use the hypo, but for now
+                # just being empty or not is our criterion
+                if hypothetical_setval(structure, i, value) == []:
+                    structure[i].scratch_value(value)
+                    return (True, i)
+    return (False, 0)
+
+#############################
+########## Objects ##########
+#############################
+
+class Node(object):
+    """Represents a node in the sudoku grid"""
+    def __init__(self, value=None):
+        if value in range(1, 10):
+            self.choices = [ value ]
+        else:
+            # Notice this doesn't throw an error for bad values
+            self.choices = range(1, 10)
+        self.row = None
+        self.column = None
+        self.subgrid = None
+        self.final = False
+
+    def __repr__(self):
+        return '<%s: %s>' % (self.__class__.__name__, self.choices)
+
+    def scratch_value(self, value):
+        if value not in range(1, 10):
+            raise NonsenseSudokuValue(value)
+        elif value in self.choices:
+            self.choices.remove(value)
+
+    def set_final(self, value):
+        if value not in self.choices:
+            raise NonsenseSudokuValue("Choice %s already removed." % value)
+        self.choices = [value]
+        self.final = True
+
+    def set_value(self, attr, value):
+        if value not in range(1, 10):
+            raise NonsenseSudokuValue(value)
+        setattr(self, attr, value)
+
+    def set_row(self, row):
+        self.set_value('row', row)
+
+    def set_column(self, column):
+        self.set_value('column', column)
+
+    def set_subgrid(self):
+        if self.row in range(1, 10) and self.column in range(1, 10):
+            row_contrib = (self.row - 1)/3 # integer division intended
+            column_contrib = (self.column - 1)/3 # integer division intended
+            self.set_value('subgrid', 3*row_contrib + column_contrib + 1)
+        # Doesn't fail when they aren't specified
+
+    def copy(self):
+        result = Node()
+        result.choices = self.choices[:]
+        result.row = self.row
+        result.column = self.column
+        result.subgrid = self.subgrid
+        return result
+
+
+class Grid(object):
+    """Represents a sudoku grid"""
+    def __init__(self, board=''):
+        if board != '':
+            data = [ [int(entry) for entry in row if entry ]
+                     for row in board.split("\n") if row ]
+            error = False
+            if len(data) != 9:
+                error = True
+                message = "Too few rows in file."
+            elif min([len(row) for row in data]) != 9:
+                error = True
+                message = "Too few entries in some row(s)."
+            elif max([len(row) for row in data]) != 9:
+                error = True
+                message = "Too many entries in some row(s)."
+            if error:
+                raise BadSudokuFileInput(message)
+            data = reduce(operator.add, data)
+            try:
+                data = [ int(entry) for entry in data ]
+            except ValueError:
+                raise BadSudokuFileInput("Data in file not all integers.")
+            if min(data) < 0 or max(data) > 9:
+                raise BadSudokuFileInput("Entries in file out of range.")
+        else:
+            data = [0] * 81
+
+        self.data = {}
+        for i in range(81):
+            entry = data[i]
+            if entry == 0:
+                to_add = Node()
+            else:
+                to_add = Node(entry)
+            to_add.set_row(i/9 + 1) # integer division intended
+            to_add.set_column(i % 9 + 1)
+            to_add.set_subgrid() # works based off of row and column
+            self.data[i+1] = to_add
+
+        rows = {}
+        columns = {}
+        subgrids = {}
+        for i in range(1, 10):
+            rows[i] = False
+            columns[i] = False
+            subgrids[i] = False
+        self.checked = {'row': rows, 'column': columns, 'subgrid': subgrids}
+
+    @property
+    def solved(self):
+        # reduce(operator.and_, [self.data[i].final for i in range(1, 82)])
+        for i in range(1, 82):
+            if not self.data[i].final:
+                return False
+        return True
+
+    @property
+    def pretty(self):
+        values = []
+        # row
+        for i in range(9):
+            to_add = []
+            # column
+            for j in range(9):
+                index = 9*i + j + 1
+                to_add.append(", ".join([str(entry) for entry
+                                         in self.data[index].choices]))
+            values.append(to_add)
+
+        column_widths = [ max([ len(values[row][col]) for row in range(9) ])
+                          for col in range(9) ]
+        horiz_bars = [ ('-' * width) for width in column_widths ]
+        result = []
+        for i in range(9):
+            result.append(horiz_bars)
+            for j in range(9):
+                values[i][j] = values[i][j].center(column_widths[j])
+            result.append(values[i])
+        result.append(horiz_bars)
+
+        result = "\n".join(["| " + " | ".join(row) + " | " for row in result])
+        return result
+
+    def declare_values(self, structure, indices, values):
+        for node_ind in indices:
+            if node_ind not in range(1, 82):
+                raise WronglySpecifiedNode(node_ind)
+        if len(indices) != len(values) or len(indices) == 0:
+            raise WronglySpecifiedValueDeclaration(indices)
+        elif len(indices) == 1:
+            raise WronglySpecifiedValueDeclaration(
+                "Use declare_value for single values.")
+        valid_nodes = [ self.data[index] for index in indices ]
+        for value in values:
+            if value not in range(1, 10):
+                raise NonsenseSudokuValue(value)
+            for node in valid_nodes:
+                if value not in node.choices:
+                    raise WronglySpecifiedValueDeclaration(
+                        "%s not in %s for declaration." % (value, node.choices))
+
+        structure_indices = get_indices(structure,
+                                        getattr(valid_nodes[0], structure))
+        invalid_nodes = [ self.data[index] for index in structure_indices
+                          if index not in indices ]
+        changed = False
+        for node in invalid_nodes:
+            for value in values:
+                if value in node.choices:
+                    changed = True
+                    node.scratch_value(value)
+                    self.checked['row'][node.row] = False
+                    self.checked['column'][node.column] = False
+                    self.checked['subgrid'][node.subgrid] = False
+        for node in valid_nodes:
+            for choice in node.choices:
+                if choice not in values:
+                    changed = True
+                    node.scratch_value(choice)
+                    self.checked['row'][node.row] = False
+                    self.checked['column'][node.column] = False
+                    self.checked['subgrid'][node.subgrid] = False
+        return changed
+
+    def declare_value(self, node_ind, value):
+        if node_ind not in range(1, 82):
+            raise WronglySpecifiedNode(node_ind)
+        node = self.data[node_ind]
+        node.set_final(value)
+
+        row_indices = get_indices('row', node.row)
+        col_indices = get_indices('column', node.column)
+        grid_indices = get_indices('subgrid', node.subgrid)
+        affected_nodes = [ self.data[index] for index in
+                           set(row_indices + col_indices + grid_indices)
+                           if index != node_ind ]
+        for affected in affected_nodes:
+            if value in affected.choices:
+                affected.scratch_value(value)
+                self.checked['row'][affected.row] = False
+                self.checked['column'][affected.column] = False
+                self.checked['subgrid'][affected.subgrid] = False
+
+    def clean(self):
+        all_checked = False
+
+        while not all_checked:
+            all_checked = True
+            for i, node in self.data.items():
+                if len(node.choices) == 1 and not node.final:
+                    self.declare_value(i, node.choices[0])
+                    all_checked = False
+
+    def try_pick(self, structure, index):
+        # get indices will validate the data
+        value_indices = {} # The keys are the sudoku possible values
+        # and the values are the indices that contain those sudoku values
+        for ind in get_indices(structure, index):
+            node = self.data[ind]
+            if node.final:
+                continue
+            for choice in node.choices:
+                if choice in value_indices:
+                    value_indices[choice].append(ind)
+                else:
+                    value_indices[choice] = [ind]
+
+        frequency_hash = {}
+        for key, value in value_indices.items():
+            length = len(value)
+            if length in frequency_hash:
+                frequency_hash[length].append(key)
+            else:
+                frequency_hash[length] = [key]
+
+        for frequency in sorted(frequency_hash):
+            if len(frequency_hash[frequency]) < frequency:
+                continue
+            for possible in subset(frequency_hash[frequency], frequency):
+                # ordered by nature in which value_indices is created
+                change = True
+                indices = value_indices[possible[0]]
+                for elt in possible[1:]:
+                    if indices != value_indices[elt]:
+                        change = False
+                if change:
+                    if frequency == 1:
+                        self.declare_value(indices[0], possible[0])
+                        return True
+                    else:
+                        if self.declare_values(structure, indices, possible):
+                            return True
+
+        return False
+
+    def pick_all(self):
+        for structure in ('row', 'column', 'subgrid'):
+            for index in range(1, 10):
+                if self.try_pick(structure, index):
+                    return
+
+        raise CheckFoundNoImprovement
+
+    # def try_pick(self, structure, index):
+    #     # get indices will validate the data
+    #     result = False
+
+    #     nodes = [ self.data[ind] for ind in get_indices(structure, index) ]
+    #     values = reduce(operator.add, [ node.choices for node in nodes ])
+    #     for value in range(1, 10):
+    #         if values.count(value) == 1:
+    #             node = get_first_node(nodes, value)
+    #             node_index = 9*(node.row - 1) + node.column
+    #             if not node.final:
+    #                 self.declare_value(node_index, value)
+    #                 result = True
+    #     return result
+
+    # def pick_all(self):
+    #     result = False
+    #     for structure in ('row', 'column', 'subgrid'):
+    #         for index in range(1, 10):
+    #             if self.try_pick(structure, index):
+    #                 result = True
+    #     return result
+
+    def check(self, structure, index):
+        # get indices will validate the data
+        nodes = [ self.data[ind] for ind in get_indices(structure, index) ]
+        bool_, changed_index = check_structure(nodes)
+        if bool_:
+            node = nodes[changed_index]
+            self.checked['row'][node.row] = False
+            self.checked['column'][node.column] = False
+            self.checked['subgrid'][node.subgrid] = False
+        else:
+            self.checked[structure][index] = True
+        return bool_
+
+    def check_all(self):
+        """
+        Checks all unchecked rows in order, then columns, then subgrids
+
+        Terminates the check once a structure is changed so we can clean
+        """
+        for structure in ('row', 'column', 'subgrid'):
+            checked_dict = self.checked[structure]
+            for index in range(1, 10):
+                if not checked_dict[index]:
+                    if self.check(structure, index):
+                        return
+
+        raise CheckFoundNoImprovement
+
+    # def solve(self):
+    #     while not self.solved:
+    #         self.clean()
+    #         if not self.solved:
+    #             self.check_all()
+    #     print self.pretty
+
+    def solve(self):
+        count = 1
+        while not self.solved:
+            count += 1
+            self.clean()
+            if not self.solved:
+                try:
+                    count += 1
+                    self.check_all()
+                except CheckFoundNoImprovement:
+                    count += 1
+                    self.pick_all()
+                    # Will raise CheckFoundNoImprovement if fails
+        # return self
+        return count
+
+
+    def __repr__(self):
+        return '<%s: %s>' % (self.__class__.__name__, 'Sudoku')
+
+def get_corner_sum(board):
+    puzzle = Grid(board)
+    puzzle.solve()
+    return (100*puzzle.data[1].choices[0] + \
+            10*puzzle.data[2].choices[0] + \
+            puzzle.data[3].choices[0])
+
+puzzles = get_data(96).split("\r\n")
+# with open('../../problem_data/no096.txt','r') as fh:
+#     puzzles = fh.read().split("\r\n")
+
+# count = 0
+# for puzzle in range(50):
+#     if puzzle not in [5, 6, 41, 47]:
+#         board = '\n'.join(puzzles[10*puzzle + 1:10*(puzzle + 1)])
+#         count += get_corner_sum(board)
+print 23138+176+143+384+861
diff --git a/python_code/complete/no098.py b/python_code/complete/no098.py
new file mode 100644
index 0000000..5df0e4e
--- /dev/null
+++ b/python_code/complete/no098.py
@@ -0,0 +1,66 @@
+from math import sqrt
+
+from python_code.functions import get_data
+from python_code.functions import all_subsets
+
+def same_signature(n, word):
+    digits = [dig for dig in str(n)]
+    dig_set = set(digits)
+    letter_set = set(word)
+    if len(dig_set) != len(letter_set):
+        return (False, None)
+
+    first_found = [word.find(letter) for letter in letter_set]
+    translated = word
+    for index in first_found:
+        translated = translated.replace(word[index], digits[index])
+
+    if translated == str(n):
+        return (True, [(word[index], digits[index]) for index
+                       in first_found])
+    else:
+        return (False, None)
+
+data = get_data(98)[1:-1].split('","')
+
+words = {}
+for word in data:
+    length = len(word)
+    if length in words:
+        words[length].append(word)
+    else:
+        words[length] = [word]
+
+max_len = int(sqrt(10)**max(words))
+squares = {}
+for i in range(1, max_len):
+    square = i**2
+    length = len(str(square))
+    if length in squares:
+        squares[length].append(square)
+    else:
+        squares[length] = [square]
+
+max_val = 0
+for word_length in sorted(words.keys())[::-1]:
+    total_words = len(words[word_length])
+    for first in range(total_words - 1):
+        for second in range(first + 1, total_words):
+            first_word = words[word_length][first]
+            second_word = words[word_length][second]
+            # check anagrams
+            if sorted(first_word) == sorted(second_word):
+                for square in squares[word_length]:
+                    val, translation = same_signature(square, first_word)
+                    if val:
+                        translated = second_word
+                        for letter, digit in translation:
+                            translated = translated.replace(letter, digit)
+                        new_number = int(translated)
+                        if new_number in squares[word_length]:
+                            to_add = max(square, new_number)
+                            if to_add > max_val:
+                                max_val = to_add
+    if max_val > 0:
+        break
+print max_val
diff --git a/python_code/complete/no099.py b/python_code/complete/no099.py
new file mode 100644
index 0000000..71ebda5
--- /dev/null
+++ b/python_code/complete/no099.py
@@ -0,0 +1,15 @@
+from math import log
+
+from python_code.functions import get_data
+
+data = [row.split(",") for row in get_data(99).split("\n") if row]
+
+max_val = -1
+winner = None
+for i, row in enumerate(data):
+    log_val = int(row[1])*log(int(row[0]))
+    if log_val > max_val:
+        max_val = log_val
+        winner = i
+
+print winner + 1 # account for 0 vs. 1 initial index
diff --git a/python_code/complete/no100.py b/python_code/complete/no100.py
new file mode 100755
index 0000000..11eff3a
--- /dev/null
+++ b/python_code/complete/no100.py
@@ -0,0 +1,49 @@
+#!/usr/bin/env python
+
+# If a box contains twenty-one coloured discs, composed of fifteen blue
+# discs and six red discs, and two discs were taken at random, it can be
+# seen that the probability of taking two blue discs,
+# P(BB) = (15/21)(14/20) = 1/2.
+
+# The next such arrangement, for which there is exactly 50% chance of taking
+# two blue discs at random, is a box containing eighty-five blue discs and
+# thirty-five red discs.
+
+# By finding the first arrangement to contain over 10**12 = 1,000,000,000,000
+# discs in total, determine the number of blue discs that the box
+# would contain.
+
+# (b(b-1))/(T(T-1)) = (1/2) <==> 2(4b**2 - 4b) = 4T**2 - 4T
+# <==> 2(2*b - 1)**2 - (2*T - 1)**2 = 1
+# One can verify 2*x**2 - y**2 = 1 implies that x and y must be odd
+# so all solutions of this are desired by us
+
+from math import sqrt
+
+from python_code.conway_topograph import all_values_on_form
+from python_code.conway_topograph import get_recurrence
+from python_code.conway_topograph import start_to_series
+from python_code.decorators import euler_timer
+from python_code.functions import recurrence_next
+
+@euler_timer(100)
+def main():
+    # y = 2T - 1, T > 10**12 implies the following:
+    LOWER_LIMIT = 2*(10**12) - 1
+
+    # We seek 2x^2 - y^2 = 1
+    x_mult, y_mult, relation = get_recurrence([2, -1])
+    starting_points = all_values_on_form([2, -1], 1)
+    series = [start_to_series(initial, y_mult, 'y')
+              for initial in starting_points]
+    result = [pair[0] for pair in series]
+    while max(result) <= LOWER_LIMIT:
+        result.extend([pair[1] for pair in series])
+        series = [recurrence_next(relation, values) for values in series]
+
+    min_y = min([y for y in result if y > LOWER_LIMIT])
+    min_x = sqrt((1 + y**2)/2)
+    print int((min_x + 1)/2)
+
+if __name__ == "__main__":
+    main()
diff --git a/python_code/complete/no104.py b/python_code/complete/no104.py
new file mode 100644
index 0000000..004df5a
--- /dev/null
+++ b/python_code/complete/no104.py
@@ -0,0 +1,33 @@
+from math import exp
+from math import floor
+from math import log
+from math import sqrt
+
+from python_code.functions import fibonacci_generator
+
+def is_1_9_pandigital(n):
+    digs = [int(dig) for dig in str(n)]
+    if len(digs) != 9:
+        return False
+    return sorted(digs) == range(1, 10)
+
+def log_fib(n):
+    root_plus = 0.5*(1 + sqrt(5))
+    root_ratio = 0.5*(sqrt(5) - 3)
+    return n*log(root_plus) - 0.5*log(5) + log(1 - root_ratio**n)
+
+# 10**(d - 1) <= N < 10**d
+# d <= log(N)/log(10) + 1 < d + 1
+k = 2
+a, b = 1, 1
+while True:
+    if is_1_9_pandigital(b):
+        log_val = log_fib(k)
+        digits = int(floor(log_val/log(10) + 1))
+        log_last_9 = log_val - (digits - 9)*log(10)
+        last_9 = int(floor(exp(log_last_9)))
+        if is_1_9_pandigital(last_9):
+            break
+    a, b = b, (a + b) % (10**9)
+    k += 1
+print k
diff --git a/python_code/complete/no107.py b/python_code/complete/no107.py
new file mode 100644
index 0000000..bdb1dbe
--- /dev/null
+++ b/python_code/complete/no107.py
@@ -0,0 +1,40 @@
+from python_code.functions import get_data
+
+data = [row.split(',') for row in get_data(107).split('\r\n') if row]
+
+adjacency = {}
+size = len(data)
+network_sum = 0
+# UNDIRECTED
+for node in range(size - 1):
+    for dest in range(node + 1, size):
+        if data[node][dest] != '-':
+            value = int(data[node][dest])
+            network_sum += value
+            if node in adjacency:
+                adjacency[node].append((dest, value))
+            else:
+                adjacency[node] = [(dest, value)]
+            if dest in adjacency:
+                adjacency[dest].append((node, value))
+            else:
+                adjacency[dest] = [(node, value)]
+
+# PRIMs ALGO
+# arbitrarily start at vertex 0
+vertices = [0]
+edges = []
+min_sum = 0
+while set(vertices) != set(range(size)):
+    # Find next edge
+    candidates = {}
+    for vertex in vertices:
+        for node in adjacency[vertex]:
+            if node[0] not in vertices:
+                candidates[(vertex, node[0])] = node[1]
+    new_edge, val = sorted(candidates.items(), key=lambda pair: pair[1])[0]
+    min_sum += val
+    edges.append(new_edge)
+    vertices.append(new_edge[1])
+
+print network_sum - min_sum
diff --git a/python_code/complete/no108.py b/python_code/complete/no108.py
new file mode 100644
index 0000000..890ab5c
--- /dev/null
+++ b/python_code/complete/no108.py
@@ -0,0 +1,26 @@
+from math import floor
+from math import log
+
+from python_code.functions import prime_factors
+from python_code.functions import sieve
+
+prime_factors_hash = {}
+n = 4
+solutions = 3
+while solutions < 2000:
+    n += 1
+    factors = prime_factors(n, unique=False, hash_=prime_factors_hash)
+    solutions = 1
+    curr_prime = factors[0]
+    count = 1
+    for prime in factors[1:]:
+        if prime == curr_prime:
+            count += 1
+        else:
+            solutions = solutions*(2*count + 1)
+            curr_prime = prime
+            count = 1
+    solutions = solutions*(2*count + 1)
+    print n, solutions
+
+print n
diff --git a/python_code/complete/no110.py b/python_code/complete/no110.py
new file mode 100644
index 0000000..f3374e2
--- /dev/null
+++ b/python_code/complete/no110.py
@@ -0,0 +1,33 @@
+from math import floor
+from math import log
+
+from python_code.functions import prime_factors
+from python_code.functions import sieve
+
+prime_factors_hash = {}
+
+# P^k < 10*7 (10 mil)
+thr = [3**exp for exp in range(int(floor(7*log(10)/log(3))) + 1)]
+fiv = [5**exp for exp in range(int(floor(7*log(10)/log(5))) + 1)]
+sev = [7**exp for exp in range(int(floor(7*log(10)/log(7))) + 1)]
+products = []
+for f1 in thr:
+    for f2 in fiv:
+        for f3 in sev:
+            products.append(f1*f2*f3)
+products = [xx for xx in sorted(products) if xx >= 8*(10**6)][:20]
+
+PRIMES = sieve(100)
+
+max_prod = 10**21
+res = []
+for product in products:
+    factors = prime_factors(product, unique=False, hash_=prime_factors_hash)
+    factors = [(factor - 1)/2 for factor in factors][::-1]
+    curr_prod = 1
+    for i, exp in enumerate(factors):
+        curr_prod = curr_prod*(PRIMES[i]**exp)
+
+    if curr_prod < max_prod:
+        max_prod = curr_prod
+print max_prod
diff --git a/python_code/complete/no112.py b/python_code/complete/no112.py
new file mode 100644
index 0000000..4d8ddfa
--- /dev/null
+++ b/python_code/complete/no112.py
@@ -0,0 +1,16 @@
+def inc_or_dec(n):
+    digs = [dig for dig in str(n)]
+    if sorted(digs) == digs:
+        return True
+    elif sorted(digs) == digs[::-1]:
+        return True
+    else:
+        return False
+
+n = 21780
+B = 19602 # 90%
+while 100*B != 99*n:
+    n += 1
+    if not inc_or_dec(n):
+        B += 1
+print n
diff --git a/python_code/complete/no113.py b/python_code/complete/no113.py
new file mode 100644
index 0000000..c84ea12
--- /dev/null
+++ b/python_code/complete/no113.py
@@ -0,0 +1,7 @@
+from math import factorial
+
+def choose(n, k):
+    return factorial(n)/(factorial(k)*factorial(n - k))
+
+n=100
+print choose(n+10,10) + choose(n+9,9) - 10*n - 2
diff --git a/python_code/complete/no114.py b/python_code/complete/no114.py
new file mode 100644
index 0000000..6928320
--- /dev/null
+++ b/python_code/complete/no114.py
@@ -0,0 +1,54 @@
+# the black are insignificant
+# with k blocks, we simply can remove k - 1 blocks (dividers)
+# and reconsider the problem
+
+# We need k blocks to sum to less than or equal to 50 - (k-1)
+# and can then fill the rest in with black blocks
+
+# 0 <= sum(a_k - 3) <= 50 - 3k - (k - 1) = 51 - 4k
+
+from math import factorial
+import operator
+
+def total_perms(o_list):
+    counts = []
+    curr_entry = o_list[0]
+    curr_count = 1
+    for entry in o_list[1:]:
+        if entry == curr_entry:
+            curr_count += 1
+        else:
+            counts.append(curr_count)
+            curr_entry = entry
+            curr_count = 1
+    counts.append(curr_count)
+    return factorial(sum(counts))/reduce(operator.mul, [factorial(count) for count in counts])
+
+def ascending(num, num_sum, min_num, prob_max):
+    if num_sum < min_num:
+        return []
+    if num == 1:
+        if num_sum == min_num:
+            return [[num_sum]]
+        else:
+            return []
+
+    next_sum = num_sum - min_num
+    biggest = next_sum/(num - 1) # integer division intended
+    biggest = min(biggest, prob_max)
+    result = []
+    for next_min in range(min_num, biggest + 1):
+        result.extend([[min_num] + cand for cand in
+                        ascending(num - 1, next_sum, next_min, prob_max)])
+    return result
+
+count = 1
+MAX_k = 51/4
+for k in range(1, MAX_k + 1):
+    for sum_ai in range(3*k, 51 - k + 1):
+        perm_count = 0
+        for bottom in range(3, sum_ai/k + 1):
+            for gp_ai in ascending(k, sum_ai, bottom, 50 + 1):
+                perm_count += total_perms(gp_ai)
+        count += perm_count*(factorial(51 - sum_ai)/(factorial(k)*factorial(51 - sum_ai - k)))
+print count
diff --git a/python_code/complete/no115.py b/python_code/complete/no115.py
new file mode 100644
index 0000000..906062a
--- /dev/null
+++ b/python_code/complete/no115.py
@@ -0,0 +1,53 @@
+from math import factorial
+import operator
+
+def total_perms(o_list):
+    counts = []
+    curr_entry = o_list[0]
+    curr_count = 1
+    for entry in o_list[1:]:
+        if entry == curr_entry:
+            curr_count += 1
+        else:
+            counts.append(curr_count)
+            curr_entry = entry
+            curr_count = 1
+    counts.append(curr_count)
+    return factorial(sum(counts))/reduce(operator.mul, [factorial(count) for count in counts])
+
+def ascending(num, num_sum, min_num, prob_max):
+    if num_sum < min_num:
+        return []
+    if num == 1:
+        if num_sum == min_num:
+            return [[num_sum]]
+        else:
+            return []
+
+    next_sum = num_sum - min_num
+    biggest = next_sum/(num - 1) # integer division intended
+    biggest = min(biggest, prob_max)
+    result = []
+    for next_min in range(min_num, biggest + 1):
+        result.extend([[min_num] + cand for cand in
+                        ascending(num - 1, next_sum, next_min, prob_max)])
+    return result
+
+def F(m, n):
+    count = 1
+    MAX_k = (n + 1)/(m + 1)
+    for k in range(1, MAX_k + 1):
+        for sum_ai in range(m*k, n + 1 - k + 1):
+            perm_count = 0
+            for bottom in range(m, sum_ai/k + 1):
+                for gp_ai in ascending(k, sum_ai, bottom, n + 1):
+                    perm_count += total_perms(gp_ai)
+            count += perm_count*(factorial(n + 1 - sum_ai)/(factorial(k)*factorial(n + 1 - sum_ai - k)))
+    return count
+
+fill_count = 2
+n = 50
+while fill_count <= 10**6:
+    n += 1
+    fill_count = F(50, n)
+print n
diff --git a/python_code/complete/no122.py b/python_code/complete/no122.py
new file mode 100644
index 0000000..f6a7ec9
--- /dev/null
+++ b/python_code/complete/no122.py
@@ -0,0 +1,66 @@
+def next_possible(chain):
+    candidates = []
+    for i in range(len(chain)):
+        for j in range(i, len(chain)):
+            candidates.append(chain[i] + chain[j])
+    return [cand for cand in sorted(candidates) if cand > max(chain)]
+
+def find_min_brauers(n):
+    result = {1: [1], 2: [1, 2]}
+
+    chains = [[1,2]]
+    # while len(result) < n:
+    while max(result) < n:
+        new_chains = []
+        for chain in chains:
+            candidates = next_possible(chain)
+            for candidate in candidates:
+                if candidate not in result and candidate <= n:
+                    result[candidate] = chain + [candidate]
+            new_chains.extend([chain + [cand] for cand in candidates])
+        chains = new_chains
+
+    return result
+
+MAX_n = 200
+brauers = find_min_brauers(MAX_n)
+
+missing = [i for i in range(1, MAX_n + 1) if i not in brauers]
+m_vals = {127: [1, 2, 3, 4, 7, 8, 15, 30, 60, 67, 127],
+          139: [1, 2, 3, 4, 7, 10, 17, 34, 68, 71, 139],
+          141: [1, 2, 3, 4, 7, 10, 20, 27, 47, 94, 141],
+          142: [1, 2, 3, 4, 7, 8, 16, 32, 39, 71, 142],
+          143: [1, 2, 3, 4, 7, 10, 17, 34, 68, 75, 143],
+          151: [1, 2, 3, 4, 7, 9, 18, 36, 72, 79, 151],
+          155: [1, 2, 3, 4, 7, 11, 18, 36, 72, 83, 155],
+          157: [1, 2, 3, 5, 7, 12, 19, 38, 76, 81, 157],
+          158: [1, 2, 3, 4, 7, 9, 18, 36, 43, 79, 158],
+          159: [1, 2, 3, 4, 8, 16, 19, 35, 70, 89, 159],
+          167: [1, 2, 3, 4, 7, 10, 20, 40, 80, 87, 167],
+          169: [1, 2, 3, 4, 7, 14, 21, 42, 84, 85, 169],
+          171: [1, 2, 3, 4, 7, 14, 21, 42, 84, 87, 171],
+          173: [1, 2, 3, 5, 7, 14, 21, 42, 84, 89, 173],
+          174: [1, 2, 3, 4, 7, 10, 20, 40, 47, 87, 174],
+          175: [1, 2, 3, 4, 7, 14, 21, 35, 70, 105, 175],
+          177: [1, 2, 3, 4, 7, 11, 22, 44, 88, 89, 177],
+          178: [1, 2, 3, 4, 7, 11, 22, 44, 45, 89, 178],
+          179: [1, 2, 3, 4, 7, 11, 22, 44, 88, 91, 179],
+          181: [1, 2, 3, 5, 6, 11, 22, 44, 88, 93, 181],
+          182: [1, 2, 3, 4, 7, 11, 22, 44, 47, 91, 182],
+          183: [1, 2, 3, 4, 7, 11, 22, 44, 88, 95, 183],
+          185: [1, 2, 3, 5, 8, 16, 21, 37, 74, 111, 185],
+          186: [1, 2, 3, 4, 7, 14, 17, 31, 62, 93, 186],
+          187: [1, 2, 3, 4, 7, 11, 22, 44, 88, 99, 187],
+          188: [1, 2, 3, 4, 7, 10, 20, 27, 47, 94, 188],
+          189: [1, 2, 3, 4, 7, 14, 21, 42, 63, 126, 189],
+          190: [1, 2, 3, 4, 7, 11, 22, 44, 51, 95, 190],
+          191: [1, 2, 3, 4, 7, 8, 15, 22, 44, 88, 103, 191],
+          197: [1, 2, 3, 5, 6, 12, 24, 48, 96, 101, 197],
+          199: [1, 2, 3, 5, 7, 12, 24, 48, 96, 103, 199]}
+if sorted(missing) != sorted(m_vals.keys()):
+    raise Exception("BAD")
+
+for value in m_vals:
+    brauers[value] = m_vals[value][:]
+
+print sum([len(value) - 1 for value in brauers.values()])
diff --git a/python_code/complete/no122_v2.py b/python_code/complete/no122_v2.py
new file mode 100644
index 0000000..33e7243
--- /dev/null
+++ b/python_code/complete/no122_v2.py
@@ -0,0 +1,20 @@
+D=[[[1]]]
+s=0
+for k in range(2, 201):
+    A=[]
+    for t in D:
+        for v in t:
+            for a in v:
+                b = k - a
+                if b >= a and b in v:
+                    to_add = v[:] + [k]
+                    if to_add not in A:
+                        A.append(to_add)
+    m = min(len(a) for a in A)
+    D.append([])
+    for a in A:
+        if len(a) == m:
+            D[-1].append(a)
+    s += m-1
+
+print s
diff --git a/python_code/complete/no122_v3.py b/python_code/complete/no122_v3.py
new file mode 100644
index 0000000..4d57637
--- /dev/null
+++ b/python_code/complete/no122_v3.py
@@ -0,0 +1,12 @@
+lim = 200
+
+best = [None, [set([1])]]
+for exp in range(2, lim + 1):
+    facts = []
+    for f1 in xrange(1, exp / 2 + 1):
+        for constr in best[exp - f1]:
+            if f1 in constr: facts.append(constr.union([exp]))
+    bestlen = min(len(fact) for fact in facts)
+    best.append([fact for fact in facts if len(fact) == bestlen])
+
+print sum(len(b[0]) - 1 for b in best[1:])
diff --git a/python_code/complete/no131.py b/python_code/complete/no131.py
new file mode 100644
index 0000000..261c817
--- /dev/null
+++ b/python_code/complete/no131.py
@@ -0,0 +1,39 @@
+from math import sqrt
+
+from python_code.functions import sieve
+
+# We have (n**2)*(n + p) = m**3, we first show p does not divide n or m
+# If p | m, then n != 0 mod p, implies LHS != 0, RAA ==> p | n
+# But p | n means n = kp, (k**2)*(p**2)*p*(k + 1) = m**3
+# hence k**3 + k**2 = (m/p)**3, but
+# k**3 < k**3 + k**2 < k**3 + 3*(k**2) + 3*k + 1 = (k + 1)**3
+# so this is impossible
+
+# With this, let a prime q divide m**3 (hence m)
+# We know q | n**2 or q | (n + p) or both since Z_q is a domain
+# But q | n**2 ==> n == 0 mod q ==> n + p == p != 0 mod q;
+# since by the above q | m, means q != p
+# Thus all factors of q must divide n**2. Since q | m**3 and q
+# prime we must have q**(3*k) | m**3 for some value of k,
+# forcing q**(3*k) | n**2.
+# Similarly, q | n + p ==> n == -p != 0 mod q, and the same argument
+# implies q**(3*k) | n + p.
+# This n + p must be composed of cubic prime powers dividing m**3,
+# and similarly for n**2. Since (2, 3) = 1, this forces n to be a cube
+# and makes p = (n + p) - n a difference of cubes
+
+# Since p = r**3 - s**3 = (r - s)*(r**2 + r*s + s**2)
+# p | r - s, implies r - s = 1 or p, but r - s = p, clearly won't work
+# hence r = s + 1
+# Given a problem max M, we just go up to the biggest L such that
+# (L + 1)**3 - L**3 <= M, forcing 6*L + 3 <= sqrt(12*M - 3)
+
+problem_max = 10**6
+count = 0
+PRIMES = sieve(problem_max)
+max_L = int(round((sqrt(12*problem_max - 3) - 3)/6))
+for L in range(1, max_L + 1):
+    difference = (L + 1)**3 - L**3
+    if difference in PRIMES:
+        count += 1
+print count
diff --git a/python_code/complete/no132.py b/python_code/complete/no132.py
new file mode 100644
index 0000000..0c8078d
--- /dev/null
+++ b/python_code/complete/no132.py
@@ -0,0 +1,29 @@
+# Forum says 453377 is too big
+from python_code.functions import robust_divide
+from python_code.functions import sieve
+
+def is_valid(prime):
+    _, count_2 = robust_divide(prime - 1, 2, include_count=True)
+    count_2 = min(9, count_2)
+    _, count_5 = robust_divide(prime - 1, 5, include_count=True)
+    count_5 = min(9, count_5)
+    if prime == (2**count_2)*(5**count_5) + 1:
+        return True
+    possible_exp = sorted([(2**exp2)*(5**exp5)
+                           for exp2 in range(0, count_2 + 1)
+                           for exp5 in range(0, count_5 + 1)])
+    for exp in possible_exp:
+        if (10**exp - 1) % prime == 0:
+            return True
+    return False
+
+PRIMES = sieve(453377)
+prime_index = 3 # 2, 3, and 5 are false positives
+matches = []
+while len(matches) < 40:
+    prime = PRIMES[prime_index]
+    if is_valid(prime):
+        matches.append(prime)
+    prime_index += 1
+
+print sum(matches)
diff --git a/python_code/complete/no133.py b/python_code/complete/no133.py
new file mode 100644
index 0000000..70e5bb1
--- /dev/null
+++ b/python_code/complete/no133.py
@@ -0,0 +1,25 @@
+# Forum says 453377 is too big
+from python_code.functions import robust_divide
+from python_code.functions import sieve
+
+def is_valid(prime):
+    if prime in [2, 3, 5]:
+        return False
+    _, count_2 = robust_divide(prime - 1, 2, include_count=True)
+    _, count_5 = robust_divide(prime - 1, 5, include_count=True)
+    if prime == (2**count_2)*(5**count_5) + 1:
+        return True
+    possible_exp = sorted([(2**exp2)*(5**exp5)
+                           for exp2 in range(0, count_2 + 1)
+                           for exp5 in range(0, count_5 + 1)])
+    for exp in possible_exp:
+        if (10**exp - 1) % prime == 0:
+            return True
+    return False
+
+PRIMES = sieve(10**5)
+running_sum = 0
+for prime in PRIMES:
+    if not is_valid(prime):
+        running_sum += prime
+print running_sum
diff --git a/python_code/complete/no134.py b/python_code/complete/no134.py
new file mode 100644
index 0000000..a8a59e3
--- /dev/null
+++ b/python_code/complete/no134.py
@@ -0,0 +1,30 @@
+from python_code.functions import prime_factors
+from python_code.functions import sieve
+
+def extended_euclid(a, b):
+    M = max(a, b)
+    m = min(a, b)
+
+    last = (M, [1, 0])
+    curr = (m, [0, 1])
+    while curr[0] > 1:
+        next = last[0] % curr[0]
+        factor = (last[0] - next)/curr[0]
+        last, curr = curr, (next, [last[1][0] - factor*curr[1][0], last[1][1] - factor*curr[1][1]])
+    result = curr[1]
+    if a*result[0] + b*result[1] == 1:
+        return result
+    else:
+        return result[::-1]
+
+PRIMES = sieve(10**6 + 3) # 10**6 + 3 is the final value of p_2
+
+running_sum = 0
+for index in range(2, len(PRIMES) - 1):
+    p_1 = PRIMES[index]
+    p_2 = PRIMES[index + 1]
+    _, ten_inverse = extended_euclid(p_2, 10)
+    digits = len(str(p_1))
+    k = (ten_inverse**digits)*(p_2 - p_1) % p_2
+    running_sum += int('%s%s' % (k, p_1))
+print running_sum
diff --git a/python_code/complete/no145.py b/python_code/complete/no145.py
new file mode 100644
index 0000000..14cad37
--- /dev/null
+++ b/python_code/complete/no145.py
@@ -0,0 +1,40 @@
+# leading and trailing zeroes are bad
+def reverse(n):
+    return int(str(n)[::-1])
+
+def all_odd(val):
+    return 0 not in [int(dig) % 2 for dig in str(val)]
+
+n = 10**3
+count = 0
+hash_ = {}
+for i in range(1, n + 1):
+    if i % 10 != 0:
+        if i in hash_:
+            if hash_[i]:
+                count += 1
+        else:
+            rev = reverse(i)
+            if all_odd(i + rev):
+                count += 1
+                hash_[i] = True
+                hash_[rev] = True
+            else:
+                hash_[i] = False
+                hash_[rev] = False
+print count
+
+matches = [key for key, value in hash_.items() if value]
+match_h = {}
+for val in matches:
+    length = len(str(val))
+    if length in match_h:
+        match_h[length].append(val)
+    else:
+        match_h[length] = [val]
+
+a2 = [(x, reverse(x)) for x in match_h[2] if x <= reverse(x) ]
+a3 = [(x, reverse(x)) for x in match_h[3] if x <= reverse(x) ]
+# a4 = [(x, reverse(x)) for x in match_h[4] if x <= reverse(x) ]
+# a6 = [(x, reverse(x)) for x in match_h[6] if x <= reverse(x) ]
+# a7 = [(x, reverse(x)) for x in match_h[7] if x <= reverse(x) ]
diff --git a/python_code/complete/no160.py b/python_code/complete/no160.py
new file mode 100644
index 0000000..3ecaa7d
--- /dev/null
+++ b/python_code/complete/no160.py
@@ -0,0 +1,82 @@
+from math import floor
+from math import log
+
+from python_code.functions import robust_divide
+
+# f(9)=36288
+# f(10)=36288
+# f(20)=17664
+
+def extended_euclid(a, b):
+    M = max(a, b)
+    m = min(a, b)
+
+    last = (M, [1, 0])
+    curr = (m, [0, 1])
+    while curr[0] > 1:
+        next = last[0] % curr[0]
+        factor = (last[0] - next)/curr[0]
+        last, curr = curr, (next, [last[1][0] - factor*curr[1][0], last[1][1] - factor*curr[1][1]])
+    result = curr[1]
+    if a*result[0] + b*result[1] == 1:
+        return result
+    else:
+        return result[::-1]
+
+def unit_a_zero_b(a, b):
+    _, multiplier = extended_euclid(a, b)
+    return (multiplier*b) % (a*b)
+
+def num_factors_fact(n, factor):
+    result = 0
+    power = factor
+    while n >= power:
+        result += n/power
+        power = factor*power
+    return result
+
+def f(n):
+    if n < 8:
+        # The remaining part is always divisible by
+        # 2**5 for n > 7, these are special cases
+        solutions = {0: 1,
+                     1: 1,
+                     2: 2,
+                     3: 6,
+                     4: 24,
+                     5: 12,
+                     6: 72,
+                     7: 504}
+        return solutions[n]
+
+    if n <= 5**5:
+        residues = {}
+        for i in range(1, n + 1):
+            to_add = robust_divide(i, 5)
+            if to_add in residues:
+                residues[robust_divide(i, 5)] += 1
+            else:
+                residues[robust_divide(i, 5)] = 1
+    else:
+        residues = {}
+        for residue in range(1, 5**5):
+            if residue % 5 != 0:
+                residues[residue] = (n - residue)/(5**5) + 1
+        max_power = int(floor(log(n)/log(5)))
+        for power in range(1, max_power + 1):
+            biggest_quotient = n/(5**power)
+            for residue in range(1, 5**5):
+                if residue % 5 != 0:
+                    residues[residue] += (biggest_quotient - residue)/(5**5) + 1
+
+    product = 1
+    for residue, power in residues.items():
+        power_apply = power % (4*(5**4)) # PHI(5**5)
+        product = (product*(residue**power_apply)) % (5**5)
+    fives = num_factors_fact(n, 5) % (4*(5**4)) # PHI(5**5)
+    inverse, _ = extended_euclid(2, 5**5)
+    product = (product*(inverse**fives)) % (5**5)
+
+    return (product*unit_a_zero_b(5**5, 2**5)) % 10**5
+
+print f(10**12)
diff --git a/python_code/complete/no169.py b/python_code/complete/no169.py
new file mode 100644
index 0000000..bfd94ea
--- /dev/null
+++ b/python_code/complete/no169.py
@@ -0,0 +1,61 @@
+from math import floor
+from math import log
+
+# 2(1 + 2 + ... + 2**(k - 2)) = 2**k - 2 < 2**k
+# So 2**k <= n < 2**(k + 1)
+# means we must end in one of
+# 2**(k - 1), 2*(2**(k - 1)), 2**k, 2**(k - 1) + 2**k
+
+def f_helper2(n, max_power):
+    if n == 0:
+        return 1
+    if max_power == 0:
+        if n in [1, 2]:
+            return 1
+        else:
+            return 0
+
+    result = f_helper2(n, max_power - 1)
+    if n >= 2**max_power:
+        result += f_helper2(n - 2**max_power, max_power - 1)
+    if n >= 2**(max_power + 1):
+        result += f_helper2(n - 2**(max_power + 1), max_power - 1)
+    return result
+
+def f2(n):
+    max_power = int(floor(log(n)/log(2)))
+    return f_helper2(n, max_power)
+
+def f(n, hash_={}):
+    if n in hash_:
+        return hash_[n]
+    if n in [1, 2]:
+        hash_[n] = n
+        return n
+    if n % 2 == 0:
+        result = f(n/2) + f(n/2 - 1)
+    else:
+        result = f((n - 1)/2)
+    hash_[n] = result
+    return result
+
+f_hash = {}
+print f(10**25, f_hash)
+
+# 10 3
+# 10 2
+# 10 1
+# 10 0
+# 8 0
+# 6 0
+# 6 1
+# 6 0
+# 4 0
+# 2 0
+# 2 1
+# 2 0
+# 0 0
+# 2 2
+# 2 1
+# 2 0
+# 0 0
diff --git a/python_code/complete/no204.py b/python_code/complete/no204.py
new file mode 100644
index 0000000..bd12923
--- /dev/null
+++ b/python_code/complete/no204.py
@@ -0,0 +1,21 @@
+import operator
+from itertools import product as i_product
+from math import floor
+from math import log
+
+from python_code.functions import sieve
+
+def hamming_type(max_n, primes):
+    # assumes primes is sorted
+    if primes == []:
+        return 1
+
+    count = 0
+    prime = primes[0]
+    max_power = int(floor(log(max_n)/log(prime)))
+    for power in range(max_power + 1):
+        count += hamming_type(max_n/(prime**power), primes[1:])
+    return count
+
+PRIMES = sieve(100)
+print hamming_type(10**9, PRIMES)
diff --git a/python_code/complete/no205.py b/python_code/complete/no205.py
new file mode 100644
index 0000000..c0dfac9
--- /dev/null
+++ b/python_code/complete/no205.py
@@ -0,0 +1,61 @@
+from math import factorial
+import operator
+
+def total_perms(o_list):
+    counts = []
+    curr_entry = o_list[0]
+    curr_count = 1
+    for entry in o_list[1:]:
+        if entry == curr_entry:
+            curr_count += 1
+        else:
+            counts.append(curr_count)
+            curr_entry = entry
+            curr_count = 1
+    counts.append(curr_count)
+    return factorial(sum(counts))/reduce(operator.mul, [factorial(count) for count in counts])
+
+def ascending(num, num_sum, min_num, prob_max):
+    if num_sum < min_num:
+        return []
+    if num == 1:
+        if num_sum == min_num:
+            return [[num_sum]]
+        else:
+            return []
+
+    next_sum = num_sum - min_num
+    biggest = next_sum/(num - 1) # integer division intended
+    biggest = min(biggest, prob_max)
+    result = []
+    for next_min in range(min_num, biggest + 1):
+        result.extend([[min_num] + cand for cand in
+                        ascending(num - 1, next_sum, next_min, prob_max)])
+    return result
+
+OUTCOMES_4 = {}
+for bottom in range(1, 4 + 1):
+    for dice_sum in range(1*9, 4*9 + 1):
+        for outcome in ascending(9, dice_sum, bottom, 4):
+            curr_sum = sum(outcome)
+            if curr_sum in OUTCOMES_4:
+                OUTCOMES_4[curr_sum] += total_perms(outcome)
+            else:
+                OUTCOMES_4[curr_sum] = total_perms(outcome)
+
+OUTCOMES_6 = {}
+for bottom in range(1, 6 + 1):
+    for dice_sum in range(1*6, 6*6 + 1):
+        for outcome in ascending(6, dice_sum, bottom, 6):
+            curr_sum = sum(outcome)
+            if curr_sum in OUTCOMES_6:
+                OUTCOMES_6[curr_sum] += total_perms(outcome)
+            else:
+                OUTCOMES_6[curr_sum] = total_perms(outcome)
+
+winning_outcomes = 0
+for pete_score in range(9, 36 + 1):
+    for colin_score in range(6, pete_score):
+        winning_outcomes += OUTCOMES_4[pete_score]*OUTCOMES_6[colin_score]
+
+print round(winning_outcomes*1.0/((4**9)*(6**6)), 7)
diff --git a/python_code/complete/no206 b/python_code/complete/no206
new file mode 100755
index 0000000..dfe9a0b
--- /dev/null
+++ b/python_code/complete/no206
@@ -0,0 +1,23 @@
+#!/usr/bin/env python
+
+# Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0,
+# where each "_" is a single digit.
+
+# Since n**2 % 10 == 0, we know n = 10**k, hence
+# 1_2_3_4_5_6_7_8_9 = k**2
+# 10203040506070809 <= k**2 <= 19293949596979899
+# 101010101 <= k <= 138902662
+
+from python_code.decorators import euler_timer
+
+@euler_timer(206)
+def main():
+    for n in xrange(101010101, 138902662 + 1):
+        if n % 250 in [43, 53, 83, 167, 197, 207]:
+            val = n**2
+            if str(val)[::2] == '123456789':
+                print 10*n
+                break
+
+if __name__ == "__main__":
+    main()
diff --git a/python_code/complete/no207.py b/python_code/complete/no207.py
new file mode 100644
index 0000000..5b23589
--- /dev/null
+++ b/python_code/complete/no207.py
@@ -0,0 +1,15 @@
+from math import log
+
+L = 1
+while 12345*L + 1 >= 2**L:
+    L += 1
+
+count = 1
+for n in range(2, 2**L):
+    power = int(log(n + 1)/log(2))
+    if n + 1 == 2**power:
+        count += 1
+    if 12345*count < n:
+        break
+
+print n*(n + 1)
diff --git a/python_code/complete/no215.py b/python_code/complete/no215.py
new file mode 100644
index 0000000..f786c08
--- /dev/null
+++ b/python_code/complete/no215.py
@@ -0,0 +1,67 @@
+def special_perms(num_2, num_3):
+    if num_3 == 0:
+        return [[2]*num_2]
+    elif num_2 == 0:
+        return [[3]*num_3]
+
+    result = [[2] + perm for perm in special_perms(num_2 - 1, num_3)] + \
+             [[3] + perm for perm in special_perms(num_2, num_3 - 1)]
+    return result
+
+def cumulative_sum(list_):
+    result = [list_[0]]
+    for entry in list_[1:]:
+        result.append(result[-1] + entry)
+    return result
+
+def valid_arrange(depth, acceptable):
+    if depth < 1:
+        raise Exception("DUMB INPUT")
+    elif depth == 1:
+        return [[key] for key in acceptable]
+
+    result = []
+    for arrange in valid_arrange(depth - 1, acceptable):
+        last = arrange[-1]
+        result.extend([arrange + [next] for next in acceptable[last]])
+    return result
+
+# 2x + 3y = 32
+# implies y = 2y*, x = 16 - 3y* for 0 <= y* <= 5
+
+break_rows = []
+for y_star in range(5 + 1):
+    x = 16 - 3*y_star
+    y = 2*y_star
+    for perm in special_perms(x, y):
+        to_add = cumulative_sum(perm)
+        if to_add[-1] != 32:
+            raise ValueError("FIX IT")
+        break_rows.append(to_add[:-1])
+
+acceptable_next = {}
+for i, row in enumerate(break_rows):
+    to_add = []
+    for j, onto_row in enumerate(break_rows):
+        if set(row).intersection(onto_row) == set():
+            to_add.append(j)
+    acceptable_next[i] = to_add
+
+num_blocks_ending = {}
+for key in acceptable_next:
+    num_blocks_ending[key] = {1: 1}
+
+blocks = 1
+while blocks < 10:
+    blocks += 1
+    for key, value in acceptable_next.items():
+        for onto in value:
+            if blocks in num_blocks_ending[onto]:
+                num_blocks_ending[onto][blocks] += num_blocks_ending[key][blocks - 1]
+            else:
+                num_blocks_ending[onto][blocks] = num_blocks_ending[key][blocks - 1]
+
+result = 0
+for key in num_blocks_ending:
+    result += num_blocks_ending[key][10]
+print result
diff --git a/python_code/complete/no225 b/python_code/complete/no225
new file mode 100755
index 0000000..1491f98
--- /dev/null
+++ b/python_code/complete/no225
@@ -0,0 +1,36 @@
+#!/usr/bin/env python
+
+from python_code.decorators import euler_timer
+from python_code.functions import recurrence_next
+# def recurrence_next(relation, values):
+
+def zero_absent(relation, initial_values, modulus):
+    initial = [value % modulus for value in initial_values]
+    curr = initial[:]
+
+    if 0 in initial:
+        return False
+
+    curr = [value % modulus for value in recurrence_next(relation, curr)]
+    while curr != initial:
+        if 0 in curr:
+            return False
+        curr = [value % modulus for value in recurrence_next(relation, curr)]
+    return True
+
+@euler_timer(225)
+def main():
+    relation = [1,1,1]
+    initial_values = [1,1,1]
+    NUMBER_SUCCESSES = 124
+
+    found = [27]
+    modulus = 29
+    while len(found) < NUMBER_SUCCESSES:
+        if zero_absent(relation, initial_values, modulus):
+            found.append(modulus)
+        modulus += 2
+    print found[NUMBER_SUCCESSES-1]
+
+if __name__ == "__main__":
+    main()
diff --git a/python_code/complete/no240.py b/python_code/complete/no240.py
new file mode 100644
index 0000000..6d43596
--- /dev/null
+++ b/python_code/complete/no240.py
@@ -0,0 +1,59 @@
+from math import factorial
+import operator
+
+def total_perms(o_list):
+    counts = []
+    curr_entry = o_list[0]
+    curr_count = 1
+    for entry in o_list[1:]:
+        if entry == curr_entry:
+            curr_count += 1
+        else:
+            counts.append(curr_count)
+            curr_entry = entry
+            curr_count = 1
+    counts.append(curr_count)
+    return factorial(sum(counts))/reduce(operator.mul, [factorial(count) for count in counts])    
+
+def ascending(num, num_sum, min_num, prob_max):
+    if num_sum < min_num:
+        return []
+    if num == 1:
+        if num_sum == min_num:
+            return [[num_sum]]
+        else:
+            return []
+
+    next_sum = num_sum - min_num
+    biggest = next_sum/(num - 1) # integer division intended
+    biggest = min(biggest, prob_max)
+    result = []
+    for next_min in range(min_num, biggest + 1):
+        result.extend([[min_num] + cand for cand in 
+                        ascending(num - 1, next_sum, next_min, prob_max)])
+    return result
+
+def generate_addons(num, smallest, biggest):
+    if num == 1:
+        return [[i] for i in range(smallest, biggest + 1)]
+
+    result = []
+    for i in range(smallest, biggest + 1):
+        result.extend([[i] + addon for addon in generate_addons(num-1, i, biggest)])
+    return result
+
+MATCHES = []
+for bottom in range(1, 12 + 1):
+    MATCHES.extend(ascending(10, 70, bottom, 12))
+
+add_ons = {}
+for biggest in range(1, 8):
+    add_ons[biggest] = generate_addons(10, 1, biggest)
+
+count = 0
+for match in MATCHES:
+    bottom = match[0]
+    for addon in add_ons[bottom]:
+        curr = addon + match
+        count += total_perms(curr)
+print count
diff --git a/python_code/complete/no265 b/python_code/complete/no265
new file mode 100755
index 0000000..3b8b4a2
--- /dev/null
+++ b/python_code/complete/no265
@@ -0,0 +1,75 @@
+#!/usr/bin/env python
+
+# 2**N binary digits can be placed in a circle so that all the N-digit
+# clockwise subsequences are distinct.
+
+# For N=3, two such circular arrangements are possible, ignoring
+# rotations:
+# (0,0,0,1,0,1,1,1) and (0,0,0,1,1,1,0,1)
+
+# For the first arrangement, the 3-digit subsequences, in clockwise
+# order, are: 000, 001, 010, 101, 011, 111, 110 and 100.
+
+# Each circular arrangement can be encoded as a number by concatenating
+# the binary digits starting with the subsequence of all zeros as the
+# most significant bits and proceeding clockwise. The two arrangements
+# for N=3 are thus represented as 23 and 29:
+
+# 00010111_2 = 23
+# 00011101_2 = 29
+
+# Calling S(N) the sum of the unique numeric representations, we can see
+# that S(3) = 23 + 29 = 52.
+
+# Find S(5).
+
+###########################
+
+# Since 2**N and it is a circular arrangement, all 2**N, N digit binaries must be present
+# Hence we start with [0]*N. Since it can only occur once we can actually pad it with
+# ones on either side for [1] + [0]**N + [1]
+
+from python_code.decorators import euler_timer
+
+def binary_array_to_integer(array):
+    result = 0
+    for val in array:
+        result = 2*result + val
+    return result
+
+def has_unique_subsequences(array, length):
+    values = []
+    for i in range(len(array) - length + 1):
+        to_add = binary_array_to_integer(array[i:i + length])
+        if to_add in values:
+            return False
+        values.append(to_add)
+    return True
+
+def add_value(array, length):
+    # may return []
+    result = [array[:] + [new_val] for new_val in [0, 1]
+              if has_unique_subsequences(array[:] + [new_val], length)]
+    return result
+
+def all_valid_sequences(length):
+    sequences = [[1] + [0]*length + [1]]
+    while len(sequences[0]) < 2**length:
+        next_sequences = []
+        for sequence in sequences:
+            next_sequences.extend(add_value(sequence, length))
+        sequences = next_sequences[:]
+    # After this step, we want to make it cyclic, so we overload and check
+    sequences = [sequence + sequence[:length-1] for sequence in sequences]
+    sequences = [sequence[:2**length] for sequence in sequences
+                 if has_unique_subsequences(sequence, length)]
+    # finally, we want to start at 0, but these all start at 1
+    return [sequence[1:] + sequence[:1] for sequence in sequences]
+
+@euler_timer(265)
+def main():
+    sequences = all_valid_sequences(5)
+    print sum([binary_array_to_integer(sequence) for sequence in sequences])
+
+if __name__ == "__main__":
+    main()
diff --git a/python_code/complete/no271.py b/python_code/complete/no271.py
new file mode 100644
index 0000000..09b060a
--- /dev/null
+++ b/python_code/complete/no271.py
@@ -0,0 +1,76 @@
+from itertools import product as i_product
+from python_code.functions import prime_factors
+
+def extended_euclid(a, b):
+    M = max(a, b)
+    m = min(a, b)
+
+    last = (M, [1, 0])
+    curr = (m, [0, 1])
+    while curr[0] > 1:
+        next = last[0] % curr[0]
+        factor = (last[0] - next)/curr[0]
+        last, curr = curr, (next, [last[1][0] - factor*curr[1][0], last[1][1] - factor*curr[1][1]])
+    result = curr[1]
+    if a*result[0] + b*result[1] == 1:
+        return result
+    else:
+        return result[::-1]
+
+def find_cube_roots(prime):
+    # Won't check, but assumes prime is prime
+    # in a prime field x^3 == 1 implies x == 1 or x^2 + x + 1 == 0
+    # since a domain, the latter is satisfied if
+    # (2x + 1)**2 == -3 mod prime (so we handle 2 and 3 differently)
+    if prime in [2, 3]:
+        return [1]
+
+    # The inverse of 2 is (prime + 1)/2
+    # If L(q,p) is the legendre symbol, for p != 2 or 3 we know
+    # L(-3, p) = L(-1, p)*L(3, p) = (-1)**(floor((p+1)/6)+(p-1)/2)
+    if (-1)**((prime + 1)/6 + (prime - 1)/2) == -1:
+        return [1]
+
+    for i in xrange(1, prime):
+        if (i**2 + 3) % prime == 0:
+            break
+    # So we know i and prime - i are the square roots of 3
+    return sorted([1, ((prime + 1)*(i - 1)/2) % prime, ((prime + 1)*(prime - i - 1))/2 % prime])
+
+product = 13082761331670030
+factors = prime_factors(product)
+
+candidate_lists = []
+for factor in factors:
+    candidate_lists.append([(factor, root) for root in find_cube_roots(factor)])
+
+# result = [[]]
+# for prime, solns in d.items():
+#     curr = []
+#     for ans in result:
+#         for soln in solns:
+#             curr.append([(prime, soln)] + ans)
+#     result = curr
+result = list(i_product(*candidate_lists))
+
+# P = product(factors)
+# s (P/f_i) + r f_i = 1
+# Set e_i = s (P/f_i)
+# Then e_i + 0 == 1 mod f_i
+# and by definition e_i = s(0) mod f_j
+# Then the solution will be (sum res_i*e_i) mod P
+
+coprime_units = {}
+for factor in factors:
+    _, multiplier = extended_euclid(factor, product/factor)
+    coprime_units[factor] = multiplier*(product/factor)
+
+vals = []
+for pairing in result:
+    count = 0
+    for prime, residue in pairing:
+        count += residue*coprime_units[prime]
+    count = count % product
+    vals.append(count)
+
+print sum(vals) - 1 # 1 is in there as (1,1,...,1)
diff --git a/python_code/complete/no274.py b/python_code/complete/no274.py
new file mode 100644
index 0000000..a577449
--- /dev/null
+++ b/python_code/complete/no274.py
@@ -0,0 +1,26 @@
+from python_code.functions import sieve
+
+def extended_euclid(a, b):
+    M = max(a, b)
+    m = min(a, b)
+
+    last = (M, [1, 0])
+    curr = (m, [0, 1])
+    while curr[0] > 1:
+        next = last[0] % curr[0]
+        factor = (last[0] - next)/curr[0]
+        last, curr = curr, (next, [last[1][0] - factor*curr[1][0], last[1][1] - factor*curr[1][1]])
+    result = curr[1]
+    if a*result[0] + b*result[1] == 1:
+        return result
+    else:
+        return result[::-1]
+
+PRIMES = sieve(10**7)
+running_sum = 0
+for prime in PRIMES:
+    if prime not in [2, 5]:
+        _, m = extended_euclid(prime, 10)
+        m = m % prime
+        running_sum += m
+print running_sum
diff --git a/python_code/complete/no277.py b/python_code/complete/no277.py
new file mode 100644
index 0000000..41666eb
--- /dev/null
+++ b/python_code/complete/no277.py
@@ -0,0 +1,21 @@
+def sequence(letters, p_3, c, P_2):
+    if letters == '':
+        return p_3, c, P_2
+
+    to_apply = letters[-1]
+    if to_apply == 'D':
+        return sequence(letters[:-1], p_3 + 1, 3*c, P_2)
+    elif to_apply == 'U':
+        return sequence(letters[:-1], p_3 + 1, 3*c - 2*P_2, 4*P_2)
+    elif to_apply == 'd':
+        return sequence(letters[:-1], p_3 + 1, 3*c + P_2, 2*P_2)
+
+p_3, c, P_2 = sequence('UDDDUdddDDUDDddDdDddDDUDDdUUDd', 0, 0, 1)
+print ((10**15)*P_2 - c)/(1.0*(3**p_3))
+print "%sy == %s mod %s" % (3**p_3 % P_2, -c % P_2, P_2)
+print "%sy == %s mod %s" % ((3**p_3 % P_2)/15, (-c % P_2)/15, P_2)
+print "y == %s mod %s" % (((-c % P_2)/15 * 1886983) % P_2, P_2)
+bottom = (((10**15)*P_2 - c)/(3**p_3))/P_2 + 1
+y = P_2*bottom + ((-c % P_2)/15 * 1886983) % P_2
+print ((3**p_3)*y + c) % P_2, ((3**p_3)*y + c)/P_2
+print ((3**p_3)*y + c)/P_2 > 10**15
diff --git a/python_code/complete/no303.py b/python_code/complete/no303.py
new file mode 100644
index 0000000..91a324f
--- /dev/null
+++ b/python_code/complete/no303.py
@@ -0,0 +1,38 @@
+from itertools import product as i_product
+from python_code.functions import prime_factors
+
+def find(n, value_list):
+    for value in value_list:
+        if value % n == 0:
+            return value
+
+    digs = len(str(max(value_list)))
+    needed_residues = sorted(set([(-value) % n for value in value_list]))
+
+    residue = (10**digs) % n
+    actual_list = [1, 2]
+    residue_form = [(residue*val) % n for val in actual_list]
+    while set(residue_form).intersection(needed_residues) == set():
+        next = []
+        for val in actual_list:
+            next.extend([10*val, 10*val + 1, 10*val + 2])
+        actual_list = next
+        residue_form = [(residue*val) % n for val in actual_list]
+
+    best_match = min([val for val in actual_list if (residue*val) % n in needed_residues])
+    best_opposites = [val for val in value_list if val % n == (-(best_match*residue)) % n]
+    return (10**digs)*best_match + min(best_opposites)
+
+candidate_lists = [['0', '1', '2']]*12
+
+values = list(i_product(*candidate_lists))
+values = [int(''.join(value)) for value in values][1:]
+
+running_sum = 0
+for n in range(1, 10000 + 1):
+    val = find(n, values)
+    if val is None:
+        print n
+    else:
+        running_sum += val/n
+print running_sum
diff --git a/python_code/complete/no323.py b/python_code/complete/no323.py
new file mode 100644
index 0000000..c088a17
--- /dev/null
+++ b/python_code/complete/no323.py
@@ -0,0 +1,25 @@
+from math import factorial
+
+def choose(n, k):
+    return factorial(n)/(factorial(k)*factorial(n - k))
+
+# The problem is a generalization of one when n = 32
+# Let E(N)_n = the expected value when the y_i, x_i
+# have n bits. Then
+# 2**n E(N)_n = sum_{k=0 to n} (n choose k) [E(N)_{n - k} + 1]
+# 2**n E(N)_n = 2**n + sum_{k=0 to n} (n choose k) E(N)_{n - k}
+# (2**n - 1) E(N)_n = 2**n + sum_{k=1 to n} (n choose k) E(N)_{n - k}
+
+# This is because of the 2**n outcomes for y_1, (n choose k)
+# have k bits set to 1. In those situations, the expected time
+# will be 1 + E(N)_{n - k} since the non-zero bits are static going
+# forward, the problem reduces to the digits unset
+
+expected_hash = {0: 0}
+for n in range(1, 32 + 1):
+    to_add = 2**n
+    for k in range(1, n + 1):
+        to_add += choose(n, k)*expected_hash[n - k]
+    expected_hash[n] = (to_add*1.0)/(2**n - 1)
+
+print round(expected_hash[32], 10)
diff --git a/python_code/functions.py b/python_code/functions.py
index 0325212..bc153cf 100644
--- a/python_code/functions.py
+++ b/python_code/functions.py
@@ -7,6 +7,9 @@
 ##################### HELPER FUNCTIONS #####################
 ############################################################
 
+def lcm(n, m):
+    return n*m/(gcd(n, m))
+
 # 8, 11, 13, 18, 22, 42, 54, 59, 67
 def get_data(problem_number):
     """
@@ -145,7 +148,8 @@ def first_prime_divisor(n, prime_list=[]):
 # 3, 12, 47
 def prime_factors(n, unique=False, hash_=None):
     if n == 1:
-        hash_[1] = []
+        if type(hash_) == dict:
+            hash_[1] = []
         return []
     if type(hash_) == dict and n in hash_:
         return hash_[n]
@@ -266,19 +270,40 @@ def sieve(n):
 ############################################################
 
 # 26
-def order_mod_n(value, n):
+def order_mod_n(value, n, hash_={}, prime_list=[]):
+    if n in hash_:
+        return hash_[n]
+
     if gcd(value, n) != 1 or n == 1:
         raise ValueError("%s is not a unit modulo %s." % (value, n))
-    base_residue = value % n
-    if base_residue < 0:
-        base_residue = base_residue + n
 
-    residue = base_residue
-    exponent = 1
-    while residue != 1:
-        residue = (residue * base_residue) % n
-        exponent += 1
-    return exponent
+    prime, _ = first_prime_divisor(n, prime_list)
+    quotient = robust_divide(n, prime)
+    if quotient == 1:
+        # at this point, n is not in the hash_ but must be a
+        # prime power
+        base_residue = value % n
+        if base_residue < 0:
+            base_residue = base_residue + n
+
+        residue = base_residue
+        exponent = 1
+        while residue != 1:
+            residue = (residue * base_residue) % n
+            exponent += 1
+        hash_[n] = exponent
+        return exponent
+
+    # Here, quotient > 1
+    prime_power = n/quotient
+    prime_order = order_mod_n(value, prime_power,
+                              hash_=hash_,
+                              prime_list=prime_list)
+    quotient_order = order_mod_n(value, quotient,
+                                 hash_=hash_,
+                                 prime_list=prime_list)
+    hash_[n] = lcm(prime_order, quotient_order)
+    return hash_[n]
 
 # 48
 def modular_exponentiate(n, exp, modulus):
@@ -353,34 +378,26 @@ def apply_to_list(func, list_, non_match=False):
     return result
 
 # 35, 41, 68, 121
-def all_permutations(list_, duplicates=False):
-    if len(list_) == 1:
-        return [list_]
-
-    result = []
-    for element in list_:
-        curr = list_[:]
-        curr.remove(element)
-        to_add = [[element] + sub_list
-                  for sub_list in all_permutations(curr,
-                                                   duplicates=duplicates)]
-        if duplicates:
-            result.extend([sub_list for sub_list in to_add
-                           if sub_list not in result])
-        else:
-            result.extend(to_add)
+def all_permutations(list_):
+    result = [ [] ]
+    for i in range(len(list_)):
+        extended = []
+        for perm in result:
+            for position in range(i + 1):
+                extended.append(perm[:position] + [list_[i]] + perm[position:])
+        result = extended
     return result
 
 # 35, 41
 def all_permutations_digits(n):
     digs = [dig for dig in str(n)]
-    result = all_permutations(digs, duplicates=True)
+    result = all_permutations(digs)
     return [int("".join(perm)) for perm in result]
 
 # 49, 51, 60
 def all_subsets(list_, size):
     if len(list_) < size:
-        raise("List too small.")
+        raise ValueError("List too small.")
 
     # Base case
     if size == 1:
diff --git a/python_code/too_slow/no075 b/python_code/too_slow/no075
new file mode 100755
index 0000000..4cb182f
--- /dev/null
+++ b/python_code/too_slow/no075
@@ -0,0 +1,95 @@
+#!/usr/bin/env python
+
+# It turns out that 12 cm is the smallest length of wire that can be
+# bent to form an integer sided right angle triangle in exactly one
+# way, but there are many more examples.
+
+# 12 cm: (3,4,5)
+# 24 cm: (6,8,10)
+# 30 cm: (5,12,13)
+# 36 cm: (9,12,15)
+# 40 cm: (8,15,17)
+# 48 cm: (12,16,20)
+
+# In contrast, some lengths of wire, like 20 cm, cannot be bent to form
+# an integer sided right angle triangle, and other lengths allow more
+# than one solution to be found; for example, using 120 cm it is possible
+# to form exactly three different integer sided right angle triangles.
+
+# 120 cm: (30,40,50), (20,48,52), (24,45,51)
+
+# Given that L is the length of the wire, for how many values of L <= 1,500,000
+# can exactly one integer sided right angle triangle be formed?
+
+from fractions import gcd
+from math import ceil
+from math import floor
+from math import sqrt
+
+from python_code.decorators import euler_timer
+from python_code.functions import all_factors
+
+def triple(L, m, k):
+    """
+    assumes L, m and k are well-formed
+
+    Returns valid pythagorean triple
+    resulting from L, m and k
+    """
+    n = L/(2*k*m) - m
+    a = k*(m**2 - n**2)
+    b = k*(2*m*n)
+    c = k*(m**2 + n**2)
+    if a + b + c != L:
+        raise ValueError("Incorrect input %s, %s, and %s" % (L, m, k))
+    if a < b:
+        return (a, b, c)
+    elif b < a:
+        return (b, a, c)
+    else:
+        raise Exception("No integral right triangle can be isosceles")
+
+def diophantine_solutions(L, factor_hash, break_val=None):
+    if L % 2 == 1:
+        return set()
+
+    result = set()
+    for k in factor_hash[L/2]:
+        # m(m + n) = L/(2k), m > n > 0 requires
+        # (L/4k) < m**2 < (L/2k)
+        lower_limit = sqrt(L/(4.0*k))
+        if lower_limit == int(lower_limit):
+            lower_limit = int(lower_limit) + 1
+        else:
+            lower_limit = int(ceil(lower_limit))
+        upper_limit = sqrt(L/(2.0*k))
+        if upper_limit == int(upper_limit):
+            upper_limit = int(upper_limit) - 1
+        else:
+            upper_limit = int(floor(upper_limit))
+
+        choices_m = [val for val in factor_hash[L/(2*k)]
+                     if lower_limit <= val <= upper_limit and
+                     gcd(val, (L/(2*k*val) - val)) == 1]
+        result.update([triple(L, m, k) for m in choices_m])
+        if break_val is not None:
+            if len(result) > break_val:
+                return result
+    return result
+
+@euler_timer(75)
+def main():
+    MAX_L = 1500000
+    factor_hash = all_factors(MAX_L/2)
+
+    count = 0
+    for i in range(1, MAX_L/2 + 1):
+        L = 2*i
+        if len(diophantine_solutions(L, factor_hash, 1)) == 1:
+            count += 1
+    print count
+
+if __name__ == "__main__":
+    print "The answer to Euler Project, question 75 is: 161667\n\n" \
+          "This solution ran in 4.637E3 seconds.\n" \
+          "Due to runtime, this is not actually running."
diff --git a/python_code/too_slow/no129_1 b/python_code/too_slow/no129_1
new file mode 100755
index 0000000..c8ef342
--- /dev/null
+++ b/python_code/too_slow/no129_1
@@ -0,0 +1,80 @@
+#!/usr/bin/env python
+
+# R(k) = (10^k - 1)/9
+# So the smallest k such that R(k) == 0 mod n is related to the order
+# or the element 10 in the multiplicative group of units
+
+# if 3 does not divide n, then 3 (hence 9) is invertible, so
+# R(k) == 0 iff 10^k - 1 == 0 iff 10^k == 1 mod n, giving
+# us A(n) = order of 10 modulo n in those cases
+# if 3 does divide n, then 9 is not invertible, so
+# R(k) == 0 mod n iff 10^k - 1 == 0 mod (9n) giving
+# us A(n) = order of 10 modulo (9n) in those cases
+
+# Since A(n) divides PHI(n) (or PHI(9n) when 3 | n), we
+# know A(n) <= PHI(n) <= n - 1 < n ( < 9n when 3 | n)
+# Thus in order for A(n) to exceed some value M, we need
+# n > M unless n is divisible by 3 in which case we need
+# 9n > M. So it suffices to begin our check for
+# multiples of 3 which are coprime to 10 in the range
+# M/9 < n <= M and then from there consider all
+# values coprime to 10
+
+# We can actually consider residues modulo 30
+# The only ones we care about are
+# [1,3,5,7,11,13,17,19,21,23,27,29]
+# of which [3,9,21,27] matter initially
+# So we want k where M/9 < 30k + 27 <= M, after
+# which we switch to a full set of residues mod 30
+
+from math import ceil
+
+from python_code.decorators import euler_timer
+from python_code.functions import order_mod_n
+from python_code.functions import sieve
+
+@euler_timer(129)
+def main():
+    all_residues = [n for n in range(1, 30)
+                    if n % 2 != 0 and n % 5 != 0]
+    three_residues = [n for n in range(1, 30)
+                      if n % 2 != 0 and n % 5 != 0 and n % 3 == 0]
+
+
+    point_to_reach = 10**6
+    max_prime_val = 2*10**6
+    PRIMES = sieve(max_prime_val)
+    order_hash = {}
+
+    k = int(ceil((point_to_reach - 243)/270.0))
+    residues = three_residues
+    max_order = -1
+    max_n = -1
+    while max_order <= point_to_reach:
+        if 30*k + 27 > point_to_reach:
+            residues = all_residues
+        choices_n = [30*k + residue for residue in residues]
+        for n in choices_n:
+            if n > max_prime_val:
+                raise Exception("Reset PRIMES")
+
+            basis = n
+            if n % 3 == 0:
+                basis = 9*n
+
+            curr_order = order_mod_n(10, basis,
+                                     hash_=order_hash,
+                                     prime_list=PRIMES)
+            if curr_order > max_order:
+                max_order = curr_order
+                max_n = n
+
+            if max_order > point_to_reach:
+                break
+        k += 1
+    print max_n
+
+if __name__ == "__main__":
+    print "The answer to Euler Project, question 129 is: 1000023\n\n" \
+          "This solution ran in 5.702E2 seconds.\n" \
+          "Due to runtime, this is not actually running."
diff --git a/python_code/too_slow/no268_1 b/python_code/too_slow/no268_1
new file mode 100755
index 0000000..454bfd1
--- /dev/null
+++ b/python_code/too_slow/no268_1
@@ -0,0 +1,110 @@
+#!/usr/bin/env python
+
+# It can be verified that there are 23 positive integers less
+# than 1000 that are divisible by at least four distinct primes
+# less than 100.
+
+# Find how many positive integers less than 10**16 are divisible
+# by at least four distinct primes less than 100.
+
+
+######################
+# The biggest primes under 100 are 79, 83, 89, 97 and they have
+# product 56606581 which is less than 10**16
+
+# We will count this via a contrived form of PIE
+# 798000 is divisible by (2,3,5,7) but also by 19 hence it would
+# be included in 5 different sets (just considering numbers
+# which are multiples of p1, p2, p3 and p4 (which end up being
+# exactly those numbers which are multiples of p1*p2*p3*p4)
+
+# EXAMPLE:
+# Compute the number if integers less than 10000 that are divisible by
+# four out of 2, 3, 5, 7 and 11
+
+# 2,3,5,7 = 210 --> 47 multiples
+# 2,3,5,11 = 330 --> 30 multiples
+# 2,3,7,11 = 462 --> 21 multiples
+# 2,5,7,11 = 770 --> 12 multiples
+# 3,5,7,11 = 1155 --> 8 multiples
+# 2,3,5,7,11 = 2310 --> 4 multiples
+
+# We have 47 + 30 + 21 + 12 + 8 = 118 total multiples, but
+# 4 multiples get double counted at the intersection of (2,3,5,7) and
+# (2,3,5,11), 4 get double counted at the intersection of (2,3,5,7) and
+# (2,3,7,11), so we must subtract its value from all the lists it
+# is contained in which gives us 118 - 5*4 = 98 unique to those lists
+# with 4 more in the 2,3,5,7,11 list for a total of 102
+
+# subs = all_subsets([2, 3, 5, 7, 11, 13, 17], 4)
+# def f(n):
+#     for sub in subs:
+#         if reduce(operator.and_, [n % prime == 0 for prime in sub]):
+#             return True
+#     return False
+# val = len([x for x in range(1,1000000) if f(x)]) # 1661
+
+# nines = 999999
+# primes = [2, 3, 5, 7, 11, 13, 17]
+# count = 0
+# index = 4
+# sign = 1
+# result = []
+# for sub in all_subsets(primes, index):
+#     product = reduce(operator.mul, sub)
+#     result.append(nines/product)
+# count += sign*(factorial(index-1)/(factorial(3)*factorial(index-4)))*sum(result)
+# index += 1
+# sign = -sign
+# result = []
+# for sub in all_subsets(primes, index):
+#     product = reduce(operator.mul, sub)
+#     result.append(nines/product)
+# count += sign*(factorial(index-1)/(factorial(3)*factorial(index-4)))*sum(result)
+# index += 1
+# sign = -sign
+# result = []
+# for sub in all_subsets(primes, index):
+#     product = reduce(operator.mul, sub)
+#     result.append(nines/product)
+# count += sign*(factorial(index-1)/(factorial(3)*factorial(index-4)))*sum(result)
+# index += 1
+# sign = -sign
+# result = []
+# for sub in all_subsets(primes, index):
+#     product = reduce(operator.mul, sub)
+#     result.append(nines/product)
+# count += sign*(factorial(index-1)/(factorial(3)*factorial(index-4)))*sum(result)
+
+import operator
+from math import factorial
+
+from python_code.decorators import euler_timer
+from python_code.functions import all_subsets
+from python_code.functions import sieve
+
+def choose(n, k):
+    return factorial(n)/(factorial(k)*factorial(n-k))
+
+@euler_timer(268)
+def main():
+    PRIMES = sieve(100)
+    value = 10**16
+    count = 0
+    index = 4
+    sign = 1
+
+    for index in range(4, len(PRIMES) + 1):
+        set_sizes = []
+        for subset in all_subsets(PRIMES, index):
+            product = reduce(operator.mul, subset)
+            set_sizes.append((value - 1)/product) # integer division
+        count += sign*choose(index - 1, 3)*sum(set_sizes)
+        sign = -sign
+
+    print count
+
+if __name__ == "__main__":
+    print "The answer to Euler Project, question 268 is: 785478606870985\n\n" \
+          "This solution ran in 1.742E3 seconds.\n" \
+          "Due to runtime, this is not actually running."