diff --git a/p011.groovy b/p011.groovy new file mode 100644 index 0000000..62fe845 --- /dev/null +++ b/p011.groovy @@ -0,0 +1,46 @@ +table = """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""" + +int[][] matrix = new int[26][26] +(0..25).each { i -> (0..25).each { j -> matrix[i][j] = 1}} + +table.split('\n').eachWithIndex { line, i -> + row = line.split(' ')*.toInteger() + row.eachWithIndex { item, j -> + matrix[i+3][j+3] = item + } +} + +max = 0 + +(0..19).each { i -> + (0..19).each { j -> + prod = matrix[i+3][j+3] * matrix[i+3][j+4] * matrix[i+3][j+5] * matrix[i+3][j+6] + if (max < prod) max = prod + prod = matrix[i+3][j+3] * matrix[i+4][j+3] * matrix[i+5][j+3] * matrix[i+6][j+3] + if (max < prod) max = prod + prod = matrix[i+3][j+3] * matrix[i+4][j+4] * matrix[i+5][j+5] * matrix[i+6][j+6] + if (max < prod) max = prod + prod = matrix[i+3][j+3] * matrix[i+4][j+2] * matrix[i+5][j+1] * matrix[i+6][j+0] + if (max < prod) max = prod + } +} +println max diff --git a/p012.erl b/p012.erl new file mode 100644 index 0000000..cfeaf29 --- /dev/null +++ b/p012.erl @@ -0,0 +1,67 @@ +%% Problem +%% --------------------- +%% The sequence of triangle numbers is generated by adding the natural numbers. +%% So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. +%% The first ten terms would be: +%% +%% 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... +%% +%% Let us list the factors of the first seven triangle numbers: +%% +%% 1: 1 +%% 3: 1,3 +%% 6: 1,2,3,6 +%% 10: 1,2,5,10 +%% 15: 1,3,5,15 +%% 21: 1,3,7,21 +%% 28: 1,2,4,7,14,28 +%% +%% We can see that 28 is the first triangle number to have over five divisors. +%% +%% What is the value of the first triangle number to have over five hundred divisors? +%% --------------------- + +-module(p012). +-export([solve1/0, solve2/0]). +-include_lib("eunit/include/eunit.hrl"). + +%% +%% Brute force solution +%% +solve2() -> triangular(7, 0). + +triangular(N, Result) when Result > 500 -> N*(N-1) div 2; +triangular(N, _) -> triangular(N+1, factors(N*(N+1) div 2)). + +%% +%% Returns number of divisors of integer N +%% +factors(N) -> factors(N, trunc(math:sqrt(N))). + +factors(N, L) when L*L == N -> factors(N, L+1) - 1; +factors(N, L) -> 2 * length([ X || X <- lists:seq(1,L), N rem X =:= 0 ]). + +%% +%% Faster solution uses the fact that +%% D(t) = D(n/2)D(n+1) (n is even) or D(t) = D(n)*D((n+1)/2) (n is odd) +%% Also reusing D(n) from previous iteration +%% +solve1() -> tri(2, 1, 1). + +tri(N, _, Result) when Result > 500 -> N*(N-1) div 2; +tri(N, D, _) -> + M = case N rem 2 == 0 of + true -> N+1; + false -> (N+1) div 2 + end, + D1 = factors(M), + tri(N+1, D1, D*D1). + + +% Tests + +factors_25_test() -> + ?assertEqual(3, factors(25)). + +factors_28_test() -> + ?assertEqual(6, factors(28)). diff --git a/p013.erl b/p013.erl new file mode 100644 index 0000000..957af54 --- /dev/null +++ b/p013.erl @@ -0,0 +1,114 @@ +%% Problem +%% --------------------- +%% Find the first ten digits of the sum of one-hundred 50-digit numbers. +%% --------------------- + +-module(p013). +-export([solve/0]). + +numbers() -> [ +37107287533902102798797998220837590246510135740250, +46376937677490009712648124896970078050417018260538, +74324986199524741059474233309513058123726617309629, +91942213363574161572522430563301811072406154908250, +23067588207539346171171980310421047513778063246676, +89261670696623633820136378418383684178734361726757, +28112879812849979408065481931592621691275889832738, +44274228917432520321923589422876796487670272189318, +47451445736001306439091167216856844588711603153276, +70386486105843025439939619828917593665686757934951, +62176457141856560629502157223196586755079324193331, +64906352462741904929101432445813822663347944758178, +92575867718337217661963751590579239728245598838407, +58203565325359399008402633568948830189458628227828, +80181199384826282014278194139940567587151170094390, +35398664372827112653829987240784473053190104293586, +86515506006295864861532075273371959191420517255829, +71693888707715466499115593487603532921714970056938, +54370070576826684624621495650076471787294438377604, +53282654108756828443191190634694037855217779295145, +36123272525000296071075082563815656710885258350721, +45876576172410976447339110607218265236877223636045, +17423706905851860660448207621209813287860733969412, +81142660418086830619328460811191061556940512689692, +51934325451728388641918047049293215058642563049483, +62467221648435076201727918039944693004732956340691, +15732444386908125794514089057706229429197107928209, +55037687525678773091862540744969844508330393682126, +18336384825330154686196124348767681297534375946515, +80386287592878490201521685554828717201219257766954, +78182833757993103614740356856449095527097864797581, +16726320100436897842553539920931837441497806860984, +48403098129077791799088218795327364475675590848030, +87086987551392711854517078544161852424320693150332, +59959406895756536782107074926966537676326235447210, +69793950679652694742597709739166693763042633987085, +41052684708299085211399427365734116182760315001271, +65378607361501080857009149939512557028198746004375, +35829035317434717326932123578154982629742552737307, +94953759765105305946966067683156574377167401875275, +88902802571733229619176668713819931811048770190271, +25267680276078003013678680992525463401061632866526, +36270218540497705585629946580636237993140746255962, +24074486908231174977792365466257246923322810917141, +91430288197103288597806669760892938638285025333403, +34413065578016127815921815005561868836468420090470, +23053081172816430487623791969842487255036638784583, +11487696932154902810424020138335124462181441773470, +63783299490636259666498587618221225225512486764533, +67720186971698544312419572409913959008952310058822, +95548255300263520781532296796249481641953868218774, +76085327132285723110424803456124867697064507995236, +37774242535411291684276865538926205024910326572967, +23701913275725675285653248258265463092207058596522, +29798860272258331913126375147341994889534765745501, +18495701454879288984856827726077713721403798879715, +38298203783031473527721580348144513491373226651381, +34829543829199918180278916522431027392251122869539, +40957953066405232632538044100059654939159879593635, +29746152185502371307642255121183693803580388584903, +41698116222072977186158236678424689157993532961922, +62467957194401269043877107275048102390895523597457, +23189706772547915061505504953922979530901129967519, +86188088225875314529584099251203829009407770775672, +11306739708304724483816533873502340845647058077308, +82959174767140363198008187129011875491310547126581, +97623331044818386269515456334926366572897563400500, +42846280183517070527831839425882145521227251250327, +55121603546981200581762165212827652751691296897789, +32238195734329339946437501907836945765883352399886, +75506164965184775180738168837861091527357929701337, +62177842752192623401942399639168044983993173312731, +32924185707147349566916674687634660915035914677504, +99518671430235219628894890102423325116913619626622, +73267460800591547471830798392868535206946944540724, +76841822524674417161514036427982273348055556214818, +97142617910342598647204516893989422179826088076852, +87783646182799346313767754307809363333018982642090, +10848802521674670883215120185883543223812876952786, +71329612474782464538636993009049310363619763878039, +62184073572399794223406235393808339651327408011116, +66627891981488087797941876876144230030984490851411, +60661826293682836764744779239180335110989069790714, +85786944089552990653640447425576083659976645795096, +66024396409905389607120198219976047599490197230297, +64913982680032973156037120041377903785566085089252, +16730939319872750275468906903707539413042652315011, +94809377245048795150954100921645863754710598436791, +78639167021187492431995700641917969777599028300699, +15368713711936614952811305876380278410754449733078, +40789923115535562561142322423255033685442488917353, +44889911501440648020369068063960672322193204149535, +41503128880339536053299340368006977710650566631954, +81234880673210146739058568557934581403627822703280, +82616570773948327592232845941706525094512325230608, +22918802058777319719839450180888072429661980811197, +77158542502016545090413245809786882778948721859617, +72107838435069186155435662884062257473692284509516, +20849603980134001723930671666823555245252804609722, +53503534226472524250874054075591789781264330331690]. + +%% +%% Dumb solution +%% +solve() -> lists:sum(numbers()). diff --git a/p014.erl b/p014.erl new file mode 100644 index 0000000..8962283 --- /dev/null +++ b/p014.erl @@ -0,0 +1,34 @@ +%% Problem +%% --------------------- +%% The following iterative sequence is defined for the set of positive integers: +%% +%% n -> n/2 (n is even) +%% n -> 3n + 1 (n is odd) +%% +%% Using the rule above and starting with 13, we generate the following sequence: +%% +%% 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 +%% +%% It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. +%% Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1. +%% +%% Which starting number, under one million, produces the longest chain? +%% --------------------- + +-module(p014). +-export([solve/0]). +-include_lib("eunit/include/eunit.hrl"). + +%% +%% Brute force solution (still relatively fast) +%% +solve() -> lists:max([ {cl(N), N} || N <- lists:seq(2,1000000) ]). + +%% +%% Chain length +%% +cl(1) -> 1; +cl(N) when N rem 2 =:= 0 -> 1 + cl(N div 2); +cl(N) -> 1 + cl(3 * N + 1). + +cl_test() -> ?assertEqual(10, cl(13)). diff --git a/p015.erl b/p015.erl new file mode 100644 index 0000000..9330565 --- /dev/null +++ b/p015.erl @@ -0,0 +1,12 @@ +%% Problem +%% --------------------- +%% Starting in the top left corner of a 2x2 grid, there are 6 routes +%% (without backtracking) to the bottom right corner. +%% +%% How many routes are there through a 20x20 grid? +%% --------------------- + +-module(p015). +-export([solve/0]). + +solve() -> mymath:c(40, 20). diff --git a/p016.erl b/p016.erl new file mode 100644 index 0000000..cd7f288 --- /dev/null +++ b/p016.erl @@ -0,0 +1,11 @@ +%% Problem +%% --------------------- +%% 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. +%% +%% What is the sum of the digits of the number 2^1000? +%% --------------------- + +-module(p016). +-export([solve/0]). + +solve() -> mymath:ds(trunc(math:pow(2,1000))). diff --git a/p018.groovy b/p018.groovy new file mode 100644 index 0000000..9a96156 --- /dev/null +++ b/p018.groovy @@ -0,0 +1,20 @@ +// inspired by +// http://blog.dreamshire.com/2009/04/01/project-euler-problem-18-solution + +// to solve problem 67 replace file name to triangle67.txt + +def max(x, y) { + x < y ? y : x +} + +triangle = [] +new File('triangle18.txt').eachLine { line -> + triangle << line.split(/ /)*.toInteger() +} +(triangle.size()-1).downto(1) { i -> + 0.upto(i-1) { j -> + triangle[i-1][j] += max(triangle[i][j], triangle[i][j+1]) + } + +} +println triangle[0][0] \ No newline at end of file diff --git a/p020.erl b/p020.erl new file mode 100644 index 0000000..039ad3e --- /dev/null +++ b/p020.erl @@ -0,0 +1,9 @@ +%% Problem +%% --------------------- +%% Find the sum of digits in 100! +%% --------------------- + +-module(p020). +-export([solve/0]). + +solve() -> mymath:ds(mymath:factorial(100)). diff --git a/p021.erl b/p021.erl new file mode 100644 index 0000000..f54f7ba --- /dev/null +++ b/p021.erl @@ -0,0 +1,31 @@ +%% Problem +%% --------------------- +%% Evaluate the sum of all the amicable numbers under 10000. +%% --------------------- + +-module(p021). +-export([solve/0]). + + +%% Brute force works relatively fast. +%% +solve() -> + Tuples = candidates(), + Amis = [ {N, D} || {N, D} <- Tuples, {N1, D1} <- Tuples, N1 =:= D, D1 =:= N ], + lists:foldl(fun({N, _}, Sum) -> N + Sum end, 0, Amis). + +candidates() -> + lists:filter(fun({N, D}) -> (D > 1) and (N =/= D) end, all_tuples()). + +all_tuples() -> + [ {N, d(N)} || N <- lists:seq(2, 10000-1) ]. + +d(N) -> + lists:sum(prop_devisors(N)). + +prop_devisors(N) -> + [ M || M <- lists:seq(1, N-1), N rem M =:= 0 ]. + + +% See also sigma function +% http://mathschallenge.net/index.php?section=faq&ref=number/sum_of_divisors \ No newline at end of file diff --git a/p022.groovy b/p022.groovy new file mode 100644 index 0000000..9b72d31 --- /dev/null +++ b/p022.groovy @@ -0,0 +1,13 @@ +def wordValue(word) { + word.bytes.inject(0) { sum, i -> sum + i - 64 } +} + +names = [] +new File('names.txt').eachLine { line -> + line.split(/,/).each { names << it[1..-2] } +} + +result = 0 +names.sort().eachWithIndex { name, i -> result += (i + 1) * wordValue(name) } + +println result \ No newline at end of file diff --git a/p025.erl b/p025.erl new file mode 100644 index 0000000..3dbdc90 --- /dev/null +++ b/p025.erl @@ -0,0 +1,33 @@ +%% Problem +%% --------------------- +%% The 12th Fibonacci number, F12, is the first term to contain three digits. +%% +%% What is the first term in the Fibonacci sequence to contain 1000 digits? +%% --------------------- + +-module(p025). +-export([solve/0, solve1/0]). + + +%% Brute force works fast. +%% +solve() -> fib(2, 1, 1, 1). + +fib(N, _, _, L) when L >= 1000 -> N; +fib(N, Fst, Snd, _) -> fib(N+1, Snd, Fst+Snd, length(integer_to_list(Fst+Snd))). + + +%% Binet's formula works only for N < 1475 +%% For greater N it throws bad argument exception +%% +solve1() -> try_next(12). + +try_next(N) -> + case length(integer_to_list(f(N))) >= 1000 of + true -> N; + false -> try_next(N+1) + end. + +f(N) -> round((math:pow(phi(), N) - math:pow(1-phi(), N)) / math:sqrt(5)). + +phi() -> (1 + math:sqrt(5)) / 2. diff --git a/p048.erl b/p048.erl new file mode 100644 index 0000000..1412ae0 --- /dev/null +++ b/p048.erl @@ -0,0 +1,21 @@ +%% Problem +%% --------------------- +%% The series, 1^1 + 2^2 + 3^3 + ... + 10^10 = 10405071317. +%% +%% Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + ... + 1000^1000. +%% --------------------- + +-module(p048). +-export([solve/0]). + + +%% Brute force works fast. +%% +solve() -> solve(10000000000). +solve(D) -> lists:sum([ pow(N, N) rem D || N <- lists:seq(1, 1000)]) rem D. + +%% math:pow/2 doesn't work for N > 143 +%% +pow(X, N) -> power(X, N, 1). +power(_, 0, Acc) -> Acc; +power(X, N, Acc) -> power(X, N - 1, X * Acc). \ No newline at end of file