I just discovered a website ( projecteuler.net ) that contains 500 Mathematics problems that can best be solved using computer programs. I tried solving a couple of them. I got some right but I discovered one Exciting thing about these problems, they are structured to determined the ability of the programmer to structure Algorithms in an efficient method(solving the problem in minimum time). When I wrote the program to solve question 3 I discovered that my computer was using up to an hour to solve it.
Please go to the site and post an efficient solution to any of the problems in any language of your choice. This is for the benefit of some of us who are beginners in programming. I am a beginner in csharp.

oboy, how far you don go for the solving and learning?

Solutions in Prolog

Problem 1
multipleOfM(M,N):-
    0 is mod(N, M). 

divisibleBy3or5(N):-
    (multipleOfM(3,N) ; multipleOfM(5,N)).


range(F,F,[F]).
range(From, To, [From|L]):-
    From < To,
    F1 is From + 1,
    range(F1, To, L).

start(R2):-
    range(1,999,L),
    include(divisibleBy3or5, L, R),
    sum_list(R,R2).


Problem 2
:- dynamic stored/1.
memo(Goal) :- ( stored(Goal) -> true ; Goal, assertz(stored(Goal)) ).

fib(0, A, _, A).
fib(N, A, B, F):-
    N1 is N - 1,
    Sum is A + B,
    fib(N1, B, Sum,F).
fib(0,1).
fib(N,F):-
    N > 0,
    N1 is N+1,
    fib(N1, 0, 1, F).

%add A to B only if B is even and return the result, else return A
addIfEven(A, B, Res):-
    (0 is mod(B, 2) ->
        Res is A + B; Res = A).

%count's upward from 0 to infinity
%get fib of count and if the result is less than the limit 
%add it else return the total so far
sumUpWhileBelow(Limit,Cnt,TotalEvenFib,R):-
    FibCnt is Cnt+1,
    memo(fib(FibCnt,FibRes)),
    (FibRes =< Limit ->
        (addIfEven(TotalEvenFib,FibRes, NewTotal),
        sumUpWhileBelow(Limit,FibCnt,NewTotal,R))
    ;
        fin(TotalEvenFib,R)
    ).
fin(R,R).

sumUpWhileBelow(N,R):-
    sumUpWhileBelow(N,0,0,R).


Problem 3

:-use_module(library(clpfd)).

% solves the problem, but super fucking slow.  Bleep!
factors(N, L):-
    findall(X, (X in 1..N, 0 #= N rem X, indomain(X)), L).

prime(P):-
    factors(P, L), L = [1, P].

solve(N, LargestPrimeFactor):-
    factors(N, Factors), include(prime, Factors, Primes), max_member(LargestPrimeFactor, Primes).


Problem 4
solve(R):-
    findall(P, get_palindromes(P), PalindromeList),
    max_list(PalindromeList, R).
get_palindromes(N):-
    between(100,999,I),
    between(I,999,J),
    N is I * J,
    palindrome(N).

palindrome(N):-
    number_codes(N, A), 
    reverse(A, B), 
    A = B.

Celebrimbor:
oboy, how far you don go for the solving and learning?

I have solved about 40 of the questions and these have taught me alone about mathematics and it has improved my problem solving skills... working on a couple more. Aiming for 50 nw.

what about u?

DonSegmond:
Solutions in Prolog

nice job man but I think it's better to post pseudocode and algorithm to your solution rather than the actual code so people who do not know your language can also benefit from ur solution.

Ogbeozioma:

I have solved about 40 of the questions and these have taught me alone about mathematics and it has improved my problem solving skills... working on a couple more. Aiming for 50 nw.
what about u?

wow nice. i have solved 10. so you are the oziomajnr on the ranking??

Celebrimbor:
wow nice. i have solved 10. so you are the oziomajnr on the ranking??

yeah I'm oziomajnr, but do u guys know the number1 guy? themark626 and the number 2 guy ope. The number 3 guy is my classmate.
I saw ur post on discreet mathematics hw far have u gone?

Ogbeozioma:


yeah I'm oziomajnr, but do u guys know the number1 guy? themark626 and the number 2 guy ope. The number 3 guy is my classmate.
I saw ur post on discreet mathematics hw far have u gone?

nope. but i would like to know him too. As for my discrete mathematics growth, well i stopped for a long time but i picked it up recently and am currently studying the principles of counting. i never really thought it was important until recently. by the way i go by the name Celebrimbor on the ranking.

Hi guys. I just found this thread. How active are you guys on Project Euler?

A similar thread exists here. https://www.nairaland.com/2286523/trivia-coding-questions-euler-project/