Problems 8-11.

10/jonm10.py

@@ -0,0 +1,18 @@
+#!/usr/bin/python
+
+import math
+
+primes = [2]
+sum = 2
+for i in xrange(3,2000000):
+    prime = True
+    for p in primes:
+        if i % p == 0:
+            prime = False
+            break
+        if p > math.sqrt(i):
+            break
+    if prime:
+        sum += i
+        primes.append(i)
+print sum

11/jonm11.py

@@ -0,0 +1,51 @@
+#!/usr/bin/python
+
+rawgrid = """08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
+49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
+81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
+52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
+22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
+24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
+32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
+67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
+24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
+21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
+78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
+16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
+86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
+19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
+04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
+88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
+04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
+20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
+20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
+01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"""
+grid = map(lambda rl: map(lambda n: int(n), rl.split(" ")),
+           rawgrid.split("\n"))
+max_prod = 1
+# left-to-right
+for row in xrange(0,20):
+    for col in xrange(0,20-3):
+        prod = (grid[row][col] * grid[row][col+1]
+                * grid[row][col+2] * grid[row][col+3])
+        max_prod = max(max_prod, prod)
+# up-and-down
+for row in xrange(0,20-3):
+    for col in xrange(0,20):
+        prod = (grid[row][col] * grid[row+1][col]
+                * grid[row+2][col] * grid[row+3][col])
+        max_prod = max(max_prod, prod)
+# northwest-to-southeast
+for row in xrange(0,20-3):
+    for col in xrange(0,20-3):
+        prod = (grid[row][col] * grid[row+1][col+1]
+                * grid[row+2][col+2] * grid[row+3][col+3])
+        max_prod = max(max_prod, prod)
+# northeast-to-southwest
+for row in xrange(0+3,20):
+    for col in xrange(0,20-3):
+        prod = (grid[row][col] * grid[row-1][col+1]
+                * grid[row-2][col+2] * grid[row-3][col+3])
+        max_prod = max(max_prod, prod)
+print max_prod
+

8/jonm.py

@@ -0,0 +1,31 @@
+#!/usr/bin/python
+
+rawdigits = """
+73167176531330624919225119674426574742355349194934
+96983520312774506326239578318016984801869478851843
+85861560789112949495459501737958331952853208805511
+12540698747158523863050715693290963295227443043557
+66896648950445244523161731856403098711121722383113
+62229893423380308135336276614282806444486645238749
+30358907296290491560440772390713810515859307960866
+70172427121883998797908792274921901699720888093776
+65727333001053367881220235421809751254540594752243
+52584907711670556013604839586446706324415722155397
+53697817977846174064955149290862569321978468622482
+83972241375657056057490261407972968652414535100474
+82166370484403199890008895243450658541227588666881
+16427171479924442928230863465674813919123162824586
+17866458359124566529476545682848912883142607690042
+24219022671055626321111109370544217506941658960408
+07198403850962455444362981230987879927244284909188
+84580156166097919133875499200524063689912560717606
+05886116467109405077541002256983155200055935729725
+71636269561882670428252483600823257530420752963450
+"""
+concat_digits = rawdigits.replace("\n","")
+max_prod = 1
+for i in xrange(len(concat_digits)-4):
+    seq = concat_digits[i:i+5]
+    prod = int(seq[0]) * int(seq[1]) * int(seq[2]) * int(seq[3]) * int(seq[4])
+    max_prod = max(max_prod, prod)
+print max_prod

9/jonm.py

@@ -0,0 +1,12 @@
+#!/usr/bin/python
+
+import math
+import sys
+
+for a in xrange(1,997):
+    for b in xrange(a+1,998):
+        for c in xrange(b+1,999):
+            if (a*a + b*b == c*c
+                and a + b + c == 1000):
+                print a * b * c
+                sys.exit(0)