Last modified on 16 September 2013, at 10:13

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]