Prolog : Project Euler 1-9

1.swi

problem1(Answer) :- aggregate(sum(N),num(N),Answer).

num(N) :- between(1,999,N), answer(N).

answer(N) :- N rem 3 =:= 0, !.
answer(N) :- N rem 5 =:= 0.

2.swi

:- use_module(library(fibonacci), [fib/2]).

problem2(Answer) :- aggregate(sum(N),fibEven(N),Answer).

fibEven(X) :-
	between(1,inf,M), N is M*3, fib(N,X),
	(X < 4000000 -> true; !, false).

3.swi

problem3(Answer) :- prime_factors(600851475143,L), max_list(L,Answer).

prime_factors(N,X) :- prime_factors(N,2,X).
prime_factors(N,P,[N])   :- N < P*P, !.
prime_factors(N,P,[P|L]) :- N rem P =:= 0, !, N1 is N//P, prime_factors(N1,P,L).
prime_factors(N,2,X)     :- !, prime_factors(N,3,X).
prime_factors(N,P,X)     :- !, plus(P,2,P1), prime_factors(N,P1,X).

4.swi

:- use_module(library(digits), [i2d/2]).

problem4(Answer) :- solve(999,999,0,Answer).

solve(99,_,Z,Z) :- !.
solve(X,Y,Z,A)  :- X*Y =< Z, !, X1 is X-1, solve(X1,X1,Z,A).
solve(X,Y,Z,A)  :- Y =:= 99, !, X1 is X-1, solve(X1,X1,Z,A).
solve(X,Y,_,A)  :- Z is X*Y, palindrome(Z), !, X1 is X-1, solve(X1,X1,Z,A).
solve(X,Y,Z,A)  :- Y1 is Y-1, solve(X,Y1,Z,A).

palindrome(N) :- i2d(N,L), reverse(L,L).

5.swi

problem5(Answer) :- solve(20,Answer).

solve(1,1) :- !.
solve(N,X) :- N1 is N-1, solve(N1,X1), X is N*X1//gcd(N,X1).

6.swi

problem6(Answer) :-
	numlist(1,100,L),
	sumlist(L,X), square(X,X1),
	maplist(square,L,Y), sumlist(Y,Y1),
	Answer is X1-Y1.

square(N,N*N).

7.swi

isPrime(N,P) :- N < P*P, !.
isPrime(N,P) :- N rem P =:= 0, !, false.
isPrime(N,P) :- P1 is P+2, isPrime(N,P1).

nextPrime(2,3) :- !.
nextPrime(P,X) :- X is P+2, isPrime(X,3), !.
nextPrime(P,X) :- P1 is P+2, nextPrime(P1,X).

primes(10001,P,P) :- !.
primes(N,P,X) :- N1 is N+1, nextPrime(P,P1), primes(N1,P1,X).

problem7(X) :- primes(1,2,X).

8.swi

:- use_module(library(digits),[i2d/2]).

problem8(Answer) :- aggregate(max(N),solve(N),Answer).

solve(X) :- findall(N,num(N),L), append(_,[A,B,C,D,E|_],L), X is A*B*C*D*E.

num(N) :- data(Data), member(L,Data), i2d(L,L1), member(N,L1).

data([73167176531330624919225119674426574742355349194934,
      96983520312774506326239578318016984801869478851843,
      85861560789112949495459501737958331952853208805511,
      12540698747158523863050715693290963295227443043557,
      66896648950445244523161731856403098711121722383113,
      62229893423380308135336276614282806444486645238749,
      30358907296290491560440772390713810515859307960866,
      70172427121883998797908792274921901699720888093776,
      65727333001053367881220235421809751254540594752243,
      52584907711670556013604839586446706324415722155397,
      53697817977846174064955149290862569321978468622482,
      83972241375657056057490261407972968652414535100474,
      82166370484403199890008895243450658541227588666881,
      16427171479924442928230863465674813919123162824586,
      17866458359124566529476545682848912883142607690042,
      24219022671055626321111109370544217506941658960408,
      07198403850962455444362981230987879927244284909188,
      84580156166097919133875499200524063689912560717606,
      05886116467109405077541002256983155200055935729725,
      71636269561882670428252483600823257530420752963450]).

9.swi

problem9(Answer) :-
	between(1,333,A),
	Bmin is A+1, Bmax is (1000-A)//2,
	between(Bmin,Bmax,B),
	C is 1000-A-B,
	A*A + B*B =:= C*C,
	Answer is A*B*C, !.