(*

* Solution to Project Euler problem 109

* Copyright (c) Project Nayuki. All rights reserved.

*

* https://www.nayuki.io/page/project-euler-solutions

* https://github.com/nayuki/Project-Euler-solutions

*)

(* Both lists are orderless but duplicates are important; they are sort of like multisets *)

points = Join[Flatten[Table[i * j, {i, 20}, {j, 3}]], {25, 50}];

doublePoints = Join[Table[i * 2, {i, 20}], {25 * 2}];

Ways[throws_, total_, maxIndex_] := Ways[throws, total, maxIndex] = (* Memoization *)

If[throws == 0,

Boole[total == 0],

If[maxIndex > 1, Ways[throws, total, maxIndex - 1], 0] +

If[points[[maxIndex]] <= total, Ways[throws - 1, total - points[[maxIndex]], maxIndex], 0]]

Sum[

If[doublePoints[[i]] <= remainingPoints,

Ways[throws, remainingPoints - doublePoints[[i]], Length[points]],

0],

{remainingPoints, 99},

{throws, 0, 2},

{i, Length[doublePoints]}]