Collection of Computer Programs on Project Euler

This is a collection of "solutions" to "Project Euler" [1] problems using Mathematica and F# side by side. (HP48 calculator UserRPL is also added whenever possible)

The purpose is to demonstrate that these two languages can be very similar, though each bears its own accent, in solving computational problems quickly and elegantly.

Problem 1Edit


Select[Range[1, 999], (Mod[#, 3] == 0 || Mod[#, 5] == 0) &] // Total


let euler_1 = List.filter (fun x -> (x % 5 = 0 || x % 3 = 0))[1 .. 999] |> List.sum 

<<0 << X 3 MOD 0 == X 5 MOD 0 == or <<X +>> IFT >> 'X' 1 999 1 SEQ>>

Problem 2Edit


Select[Fibonacci /@ Range[1, NestWhile[(# + 1) &, 1, Fibonacci[#] <= 4*^6 &]-1], Mod[#, 2] == 0 &] // Total


let fib = Seq.unfold (fun (i,j) -> Some(i, (j,i+j))) (1,1)

let euler_2 = Seq.filter (fun x -> (x%2=0)) (fib |> Seq.takeWhile (fun n -> n<= 4000000)) |>  Seq.sum

Problem 3Edit


FactorInteger[600851475143][[All, 1]] // Max
Another Version:
FactorInteger[600851475143][[-1]][[1]]



let factor_integer (n:int64) = 
    let rec find_factor acc (n_p:int64) num =        
        if num < n_p then
            acc
        elif num % n_p = 0L then 
            find_factor (n_p::acc) n_p (num/n_p)
        else 
            find_factor acc (n_p + 1L) num
    find_factor [] 2L n

let euler_3 = Seq.max (factor_integer 600851475143L)


Problem 4Edit


Select[Outer[Times, Range[100, 999], Range[100, 999]] // Flatten, (Reverse[IntegerDigits[#]] == IntegerDigits[#]) &] // Max


A more faster version:
Max[ToExpression[Cases[Map[ToString, Union[Flatten[Table[x Table[y, {y, 100, 999}], {x, 100, 999}]]]], _?(# == StringReverse[#] &)]]]


 let integer_digits (n:int) = 
     let rec intdig (n: int) = 
         match n with
             | 0 -> []
             | _ -> (n%10)::(intdig (n/10))
    List.rev (intdig n)
     
 let isPalindrome n = 
     (integer_digits n) = ((integer_digits n) |> List.rev)
     
 let euler_4 = [for x in 100..999 do
                 for y in 100..999 do
                     if isPalindrome (x*y) then yield x*y] |> List.max
 


Let palindrome x = let digits = show x in digits == reverse digits

maximum[x*y|x<-[100..999],y<-[100..999],palindrome(x*y)]


Problem 5Edit


LCM @@ Range[1, 20]


open System.Numerics

let lcm x y =
  if x = 0I || y = 0I then 0I
  else (x / (BigInteger.GreatestCommonDivisor (x,y))) * y      
  
let euler_5 = [1I .. 20I] |> List.fold lcm 1I

Problem 6Edit


Total[Range[1, 100]]^2 - Total[#^2 & /@ Range[1, 100]]


let euler_6 = (List.sum [1..100]|>(fun x-> x*x)) - (List.sum (List.map (fun x-> x*x) [1..100]))

Problem 7Edit


Prime[10001]



let isPrime (n:int64) = 
  { 2L..(int64 (sqrt (float n))) } |> Seq.forall (fun x -> n%x <> 0L)

let primes = 
  { 2L..System.Int64.MaxValue } |> Seq.filter isPrime 
  

let euler_7 = primes |> Seq.nth 10000

Problem 8Edit


txt = "73167176531330624919225119674426574742355349194934
  96983520312774506326239578318016984801869478851843
  85861560789112949495459501737958331952853208805511
  12540698747158523863050715693290963295227443043557
  66896648950445244523161731856403098711121722383113
  62229893423380308135336276614282806444486645238749
  30358907296290491560440772390713810515859307960866
  70172427121883998797908792274921901699720888093776
  65727333001053367881220235421809751254540594752243
  52584907711670556013604839586446706324415722155397
  53697817977846174064955149290862569321978468622482
  83972241375657056057490261407972968652414535100474
  82166370484403199890008895243450658541227588666881
  16427171479924442928230863465674813919123162824586
  17866458359124566529476545682848912883142607690042
  24219022671055626321111109370544217506941658960408
  07198403850962455444362981230987879927244284909188
  84580156166097919133875499200524063689912560717606
  05886116467109405077541002256983155200055935729725
  71636269561882670428252483600823257530420752963450";

data = StringCases[txt, DigitCharacter] // ToExpression;

Map[Times @@ # &, Partition[data, 5, 1]] // Max


let txt = "73167176531330624919225119674426574742355349194934
  96983520312774506326239578318016984801869478851843
  85861560789112949495459501737958331952853208805511
  12540698747158523863050715693290963295227443043557
  66896648950445244523161731856403098711121722383113
  62229893423380308135336276614282806444486645238749
  30358907296290491560440772390713810515859307960866
  70172427121883998797908792274921901699720888093776
  65727333001053367881220235421809751254540594752243
  52584907711670556013604839586446706324415722155397
  53697817977846174064955149290862569321978468622482
  83972241375657056057490261407972968652414535100474
  82166370484403199890008895243450658541227588666881
  16427171479924442928230863465674813919123162824586
  17866458359124566529476545682848912883142607690042
  24219022671055626321111109370544217506941658960408
  07198403850962455444362981230987879927244284909188
  84580156166097919133875499200524063689912560717606
  05886116467109405077541002256983155200055935729725
  71636269561882670428252483600823257530420752963450" 
  
let data = txt |> Seq.toList |> List.filter System.Char.IsDigit |> List.map System.Char.GetNumericValue

let rec partition_5 l = 
   match l with
   | x1::(x2::x3::x4::x5::_ as t) -> [x1;x2;x3;x4;x5]::(partition_5 t)
   | _ -> []

let euler_8 = List.map (fun x -> List.fold (*) 1.0 x) (partition_5 data) |> List.max

Problem 9Edit


a*b*c /. (FindInstance[a^2 + b^2 == c^2 && a + b + c == 1000 && c > b > a > 0, {a, b, c},Integers])


let triples = seq {for a in 1..1000 do for b in 1..1000 do for c in 1..1000 -> (a,b,c)}

let (a,b,c) = Seq.find (fun (a,b,c) -> (a*a+b*b = c*c)&&(a+b+c=1000)) triples

let euler_9 = a*b*c

Problem 10Edit


(Prime /@ Range[1, NestWhile[(# + 1) &, 1, Prime[#] < 2*^6 &] - 1]) // Total


let euler_10 = primes |> Seq.takeWhile (fun elem -> elem < 2000000L) |> Seq.sum

Problem 11Edit


mm = {{8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8}, {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0}, {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65}, {52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 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, 3, 45, 2, 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, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21}, {24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72}, {21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95}, {78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92}, {16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57}, {86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58}, {19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40}, {4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66}, {88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69}, {4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36}, {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16}, {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54}, {1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}};

cord[{k_, n_}] := Module[
  {boundary, temp},
  boundary[{a_, b_}] := 21 > a > 0 && 21 > b > 0;
  temp = {{k, n + #} & /@ {0, 1, 2, 3}, {k + #, n} & /@ {0, 1, 2,
      3}, {k + #, n + #} & /@ {0, 1, 2, 3}, {{k + 3, n}, {k + 2,
      n + 1}, {k + 1, n + 2}, {k, n + 3}}};
  temp = Select[temp, And @@ (boundary /@ #) &];
  Times @@ Extract[mm, #] & /@ temp
  ]

cord /@ (Outer[List, Range[1, 20], Range[1, 20]] // Flatten[#, 1] &) //
   Flatten // Max


let text =  @"          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";
             

let cell = text |> String.split ['\n']|> List.map (String.split [' '] >> List.map int )

let rec findPatterns (cells : int list list) =
    match cells with
    | (a11::(a12::a13::a14::_ as t1))::
      ((a21::(a22::a23::  _::_ as t2))::
      (a31::(a32::a33::  _::_ as t3))::
      (a41::(  _::  _::a44::_ as t4))::_ as t5) -> let h = a11*a12*a13*a14
                                                   let v = a11*a21*a31*a41
                                                   let d1 = a11*a22*a33*a44
                                                   let d2 = a41*a32*a23*a14
                                                   [h; v; d1; d2] ::
                                                     (findPatterns [t1; t2; t3; t4] @ (findPatterns t5))
    | _ -> [[]] 
    
let euler11 =
    cell |> findPatterns |> List.concat |> List.max

Problem 12Edit



Binomial[NestWhile[(# + 1) &, 0, ((Length@Divisors @ Binomial[# + 1, 2]) <= 500) &] + 1, 2]



let factor_integer_2 n = 
    let rec find_factor acc n_p num =        
        if num < n_p then
            acc
        elif num % n_p = 0 then 
            find_factor (n_p::acc) n_p (num/n_p)
        else 
            find_factor acc (n_p + 1) num
    find_factor [] 2 n

let divisor_count n =
    if n = 1 then 1
    else
        let a = factor_integer_2 n
        a |> Seq.countBy (fun x-> x) |> Seq.map (fun (a,b) -> b+1) |> Seq.reduce (*) 
    
  
let triangles = 
  Seq.unfold (fun (c,n) -> Some(n+c, (n+c, n+1))) (0, 1)    

    
let euler12 = Seq.find (fun x -> divisor_count x > 500) triangles


Problem 13Edit



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};

Total[numbers] // IntegerDigits // #[[1 ;; 10]] &



let euler13 = List.sum [37107287533902102798797998220837590246510135740250N;
46376937677490009712648124896970078050417018260538N;
74324986199524741059474233309513058123726617309629N;
91942213363574161572522430563301811072406154908250N;
23067588207539346171171980310421047513778063246676N;
89261670696623633820136378418383684178734361726757N;
28112879812849979408065481931592621691275889832738N;
44274228917432520321923589422876796487670272189318N;
47451445736001306439091167216856844588711603153276N;
70386486105843025439939619828917593665686757934951N;
62176457141856560629502157223196586755079324193331N;
64906352462741904929101432445813822663347944758178N;
92575867718337217661963751590579239728245598838407N;
58203565325359399008402633568948830189458628227828N;
80181199384826282014278194139940567587151170094390N;
35398664372827112653829987240784473053190104293586N;
86515506006295864861532075273371959191420517255829N;
71693888707715466499115593487603532921714970056938N;
54370070576826684624621495650076471787294438377604N;
53282654108756828443191190634694037855217779295145N;
36123272525000296071075082563815656710885258350721N;
45876576172410976447339110607218265236877223636045N;
17423706905851860660448207621209813287860733969412N;
81142660418086830619328460811191061556940512689692N;
51934325451728388641918047049293215058642563049483N;
62467221648435076201727918039944693004732956340691N;
15732444386908125794514089057706229429197107928209N;
55037687525678773091862540744969844508330393682126N;
18336384825330154686196124348767681297534375946515N;
80386287592878490201521685554828717201219257766954N;
78182833757993103614740356856449095527097864797581N;
16726320100436897842553539920931837441497806860984N;
48403098129077791799088218795327364475675590848030N;
87086987551392711854517078544161852424320693150332N;
59959406895756536782107074926966537676326235447210N;
69793950679652694742597709739166693763042633987085N;
41052684708299085211399427365734116182760315001271N;
65378607361501080857009149939512557028198746004375N;
35829035317434717326932123578154982629742552737307N;
94953759765105305946966067683156574377167401875275N;
88902802571733229619176668713819931811048770190271N;
25267680276078003013678680992525463401061632866526N;
36270218540497705585629946580636237993140746255962N;
24074486908231174977792365466257246923322810917141N;
91430288197103288597806669760892938638285025333403N;
34413065578016127815921815005561868836468420090470N;
23053081172816430487623791969842487255036638784583N;
11487696932154902810424020138335124462181441773470N;
63783299490636259666498587618221225225512486764533N;
67720186971698544312419572409913959008952310058822N;
95548255300263520781532296796249481641953868218774N;
76085327132285723110424803456124867697064507995236N;
37774242535411291684276865538926205024910326572967N;
23701913275725675285653248258265463092207058596522N;
29798860272258331913126375147341994889534765745501N;
18495701454879288984856827726077713721403798879715N;
38298203783031473527721580348144513491373226651381N;
34829543829199918180278916522431027392251122869539N;
40957953066405232632538044100059654939159879593635N;
29746152185502371307642255121183693803580388584903N;
41698116222072977186158236678424689157993532961922N;
62467957194401269043877107275048102390895523597457N;
23189706772547915061505504953922979530901129967519N;
86188088225875314529584099251203829009407770775672N;
11306739708304724483816533873502340845647058077308N;
82959174767140363198008187129011875491310547126581N;
97623331044818386269515456334926366572897563400500N;
42846280183517070527831839425882145521227251250327N;
55121603546981200581762165212827652751691296897789N;
32238195734329339946437501907836945765883352399886N;
75506164965184775180738168837861091527357929701337N;
62177842752192623401942399639168044983993173312731N;
32924185707147349566916674687634660915035914677504N;
99518671430235219628894890102423325116913619626622N;
73267460800591547471830798392868535206946944540724N;
76841822524674417161514036427982273348055556214818N;
97142617910342598647204516893989422179826088076852N;
87783646182799346313767754307809363333018982642090N;
10848802521674670883215120185883543223812876952786N;
71329612474782464538636993009049310363619763878039N;
62184073572399794223406235393808339651327408011116N;
66627891981488087797941876876144230030984490851411N;
60661826293682836764744779239180335110989069790714N;
85786944089552990653640447425576083659976645795096N;
66024396409905389607120198219976047599490197230297N;
64913982680032973156037120041377903785566085089252N;
16730939319872750275468906903707539413042652315011N;
94809377245048795150954100921645863754710598436791N;
78639167021187492431995700641917969777599028300699N;
15368713711936614952811305876380278410754449733078N;
40789923115535562561142322423255033685442488917353N;
44889911501440648020369068063960672322193204149535N;
41503128880339536053299340368006977710650566631954N;
81234880673210146739058568557934581403627822703280N;
82616570773948327592232845941706525094512325230608N;
22918802058777319719839450180888072429661980811197N;
77158542502016545090413245809786882778948721859617N;
72107838435069186155435662884062257473692284509516N;
20849603980134001723930671666823555245252804609722N;
53503534226472524250874054075591789781264330331690N;]



Problem 14Edit



hailstoneLength[1] = 1;
hailstoneLength[2] = 2;
hailstoneLength[n_?EvenQ]:= hailstoneLength[n] = hailstoneLength[n/2] + 1;
hailstoneLength[n_?OddQ]:= hailstoneLength[n] = hailstoneLength[3 n + 1] + 1;

Sort[{#, hailstoneLength[#]}& /@ Range[1, 10^6], #1[[2]] > #2[[2]] &][[1]]


let rec hailstone_length (n:int64) =
    match n with
    | 1L -> 1L
    | 2L -> 2L
    | _ when n%2L=0L -> 1L + hailstone_length (n/2L)
    | _ -> 1L + hailstone_length (3L*n+1L) 


let euler14 = List.map (fun x -> (x,hailstone_length x)) [2L .. 1000000L] |> List.maxBy (fun x -> snd x)


Problem 15Edit



Binomial[40, 20]



let binomial (n:bigint) (k:bigint) =
    (List.reduce (*) [1I..n])/(List.reduce (*) [1I..k])/(List.reduce (*) [1I..(n-k)])

let euler15 = binomial 40I 20I

Problem 16Edit


IntegerDigits[2^1000] // Total



let euler16 = 
        let a = BigInteger.Pow (2I, 1000)
        a.ToString() |> Seq.toList |> List.map System.Char.GetNumericValue |> List.sum  



Problem 17Edit



dict1 = StringLength[{"one", "two", "three", "four", "five", "six",
    "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen",
    "fourteen", "fifteen", "sixteen", "seventeen", "eighteen",
    "nineteen", "twenty"}];

dict2 = StringLength[{"twenty", "thirty", "forty", "fifty", "sixty",
    "seventy", "eighty", "ninety"}];

countNumber[n_] := Module[{},
  Which[20 >= n >= 1, dict1[[n]],
   100 > n > 20, dict2[[Quotient[n, 10] - 1]] + countNumber[Mod[n, 10]],
   1000 > n >= 100, dict1[[Quotient[n, 100]]] +
    If[Mod[n, 100] == 0, StringLength["hundred"],
     StringLength["hundredand"] + countNumber[Mod[n, 100]]],
   n == 1000, StringLength["onethousand"],
   n == 0, 0,
   True, "out of range"]]

countNumber /@ Range[1, 1000] // Total


let dict1 = Array.map String.length [|"one"; "two"; "three"; "four"; "five"; "six"; "seven"; "eight"; "nine"; "ten"; "eleven"; "twelve"; "thirteen"; 
    "fourteen"; "fifteen"; "sixteen"; "seventeen"; "eighteen";  "nineteen"; "twenty"|]

let dict2 = Array.map String.length [|"twenty"; "thirty"; "forty"; "fifty"; "sixty"; "seventy"; "eighty"; "ninety"|]

let rec count_number n =
    if 20>=n && n>=1 then dict1.[n-1]
    else if 100>n && n>20 then dict2.[(n/10)-2]+ (count_number (n%10))
    else if 1000>n && n>=100 then dict1.[n/100-1]+
        if (n%100=0) then String.length "hundred"
        else String.length "hundredand" + (count_number (n%100))
    else if n=1000 then String.length "onethousand"
    else if n=0 then 0
    else 0 

let euler17 = List.map count_number [1..1000] |> List.sum



Problem 18Edit



c = Reverse[{{75}, {95, 64}, {17, 47, 82}, {18, 35, 87, 10}, {20, 4, 82, 47, 65}, {19, 1, 23, 75, 3, 34}, {88, 2, 77, 73, 7, 63, 67},
      {99, 65, 4, 28, 6, 16, 70, 92}, {41, 41, 26, 56, 83, 40, 80, 70, 33}, {41, 48, 72, 33, 47, 32, 37, 16, 94, 29}, {53, 71, 44,
     65, 25, 43, 91, 52, 97, 51, 14}, {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57},
     {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48}, {63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31},
     {4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23}}];

Fold[ Max /@ (Partition[#1, 2, 1] + #2) &, c[[1]], c[[2 ;;]]]


let tw= [[75];
        [95; 64];
        [17; 47; 82];
        [18; 35; 87; 10];
        [20; 04; 82; 47; 65];
        [19; 01; 23; 75; 03; 34];
        [88; 02; 77; 73; 07; 63; 67];
        [99; 65; 04; 28; 06; 16; 70; 92];
        [41; 41; 26; 56; 83; 40; 80; 70; 33];
        [41; 48; 72; 33; 47; 32; 37; 16; 94; 29];
        [53; 71; 44; 65; 25; 43; 91; 52; 97; 51; 14];
        [70; 11; 33; 28; 77; 73; 17; 78; 39; 68; 17; 57];
        [91; 71; 52; 38; 17; 14; 91; 43; 58; 50; 27; 29; 48];
        [63; 66; 04; 68; 89; 53; 67; 30; 73; 16; 69; 87; 40; 31];
        [04; 62; 98; 27; 23; 09; 70; 98; 73; 93; 38; 53; 60; 04; 23]]

let tw2 = List.rev tw

let crunch (a:int list) (b: int list) =
    let rec partition_2_1 x =
        match x with
        | (a::b::c) -> (max a b)::(partition_2_1 (b::c))
        | _ -> []    
    let temp = partition_2_1 a
    List.zip b temp |> List.map (fun (a,b) -> a+b)


let euler18 = List.fold crunch tw2.Head tw2.Tail




Problem 19Edit


<< Calendar`

DayOfWeek /@ (Outer[List, Range[1901, 2000], Range[1, 12], {1}] // Flatten[#, 2] &) // Cases[#, Sunday] & // Length


open System

let startDate = new DateTime(1901, 1, 1)

let euler19 = startDate 
              |> Seq.unfold (fun (x : DateTime) -> Some(x, x.AddMonths(1))) 
              |> Seq.takeWhile (fun (x : DateTime) -> x.Year < 2001) 
              |> Seq.filter (fun (x : DateTime) -> x.DayOfWeek = DayOfWeek.Sunday)
              |> Seq.length




Problem 20Edit



IntegerDigits[100!] // Total


open System.Numerics

let kk = List.reduce (*) [1I..100I]

let integer_digits_2 (n:bigint) =
        let rec intdiv (n:bigint) =             
            match BigInteger.DivRem(n,10I) with
            | (a,b) when a=0I -> [b]
            | (a,b) -> b::(intdiv a)
        List.rev (intdiv n)    
        
let euler20 = integer_digits_2 kk |> List.reduce (+)



Problem 21Edit




amicable[n_] := Module[{ds},
  ds[k_] := DivisorSigma[1, k] - k;
  ds[ds[n]] == n && ds[n] != n]

 Select[Range[2, 10000], amicable] // Total


let divisors n = 
    let rec find_factor acc n_p num =        
        if num <= n_p then
            acc
        elif num % n_p = 0 then 
            find_factor (n_p::acc) (n_p+1) num
        else 
            find_factor acc (n_p + 1) num
    find_factor [] 1 n
    
let divisor_sum n =
    List.sum (divisors n)
    
    
let amicable n =
    let k = divisor_sum n
    (divisor_sum k)=n  && (k <> n)

let euler21 = List.filter amicable [2..10000]  |> List.sum

Problem 22Edit



SetDirectory[NotebookDirectory[]]

data = Import["names.txt", "CSV"] // Flatten;

MapIndexed[First[#2]* Total[(ToCharacterCode[#1] - ToCharacterCode["A"][[1]] + 1)] &, Sort[data]] // Total



open System.IO

let euler22 =
    let names = File.ReadAllText(@"C:\names.txt").Split([|','|]) |> Array.sort    
    let char_val (x:char) = 1 + (int x)-(int 'A')
    let score (i, (x:string)) =
        let t = x.Replace("\"","")
        i * (Array.map char_val (t.ToCharArray()) |> Array.sum)
    Array.zip [|1..names.Length|] names |> Array.map score |> Array.sum


Problem 23Edit




abundant[x_] := DivisorSigma[1, x] > 2 x

abList = Select[Range[1, 28123], abundant];

isSum[checkList_, x_] :=
 If[checkList == {}, False,
  If[First[checkList] > x, False,
   If[MemberQ[abList, x - First[checkList]], True,
    isSum[Rest[checkList], x]]]]

f[sum_, x_] := If[isSum[abList, x], sum, x + sum]

Block[{$IterationLimit = 30000},
  Fold[f, 0, Range[1, 28123]]] // Timing



let divisors n = 
    let rec find_factor acc n_p num =        
        if num <= n_p then
            acc
        elif num % n_p = 0 then 
            find_factor (n_p::acc) (n_p+1) num
        else 
            find_factor acc (n_p + 1) num
    find_factor [] 1 n
    
let abundant x =
        let sum = Seq.fold (+) 0 (divisors x)
        (sum  > x)
    
let euler23 =  
    let abNumberLookup = [| for i in 0..28123 -> abundant i|]      
    let abdList = List.filter abundant [1 .. 28123]
    let rec isPairOfAb (h::t) x =
        if h >= x then false
        elif abNumberLookup.[x - h] then true
        else isPairOfAb t x       
    
    let nonPairOfAb = List.filter (fun i -> not (isPairOfAb abdList i)) [1 .. 28123]
    
    List.reduce (+) nonPairOfAb


Problem 24Edit



Permutations[Range[0, 9]][[1000000]]



let factorial n = List.reduce (*) [1..n]

let divrem n r = (n/r,n%r)

let rec perm (n:int) (s:string) =
    if s.Length = 1 then s
    else
     let (q, r) = divrem n (factorial (s.Length - 1)) 
     s.[q].ToString() + perm r (s.[..(q-1)]+s.[(q+1)..])
     

let euler24 = perm 999999 "0123456789"     

Problem 25Edit



NestWhile[(# + 1) &, 0, Length[IntegerDigits[Fibonacci[#]]] < 1000 &]



open System.Numerics

let euler25 = ((1I,1I)|> Seq.unfold (fun (a,b) -> if(a > BigInteger.Pow(10I, 999I)) then None else Some(a+b, (b,a+b))) |> Seq.length)+1


Problem 26Edit



lst = Table[Length@First@Flatten[RealDigits[1/i], 1], {i, 1, 999}];
Position[lst, Max@lst]

Last modified on 16 September 2013, at 10:13