Prolog : Project Euler 1-9

1.swi

problem1(Answer) :- findall(N,num(N),L), sumlist(L,Answer).

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

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

2.swi

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

problem2(Answer) :- findall(N,fibEven(N),L), sumlist(L,Answer).

step(N,X) :- N = X; plus(3,N,N1), step(N1,X).

fibEven(X) :- step(3,N), fib(N,X), (X < 4000000 -> true; !, false).

3.swi

:- use_module(library(primes), [primeFactors/2]).

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

4.swi

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

problem4(Answer) :-
	flag(answer,_,0),
	forall(num(answer,N),flag(answer,_,N)),
	flag(answer,Answer,Answer).

num(Flag,N) :-
	between(1,900,A), A1 is 1000-A, between(A1,999,B), N is A1*B,
	flag(Flag,X,X), N > X, i2d(N,L), reverse(L,L).

/* Another solution.

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

problem4(Answer) :- problem4(999,999,0,Answer), !.
problem4(99,_,A,A).
problem4(X,Y,Z,A) :- (X*Y =< Z; Y =:= 99), X1 is X-1, problem4(X1,X1,Z,A).
problem4(X,Y,_,A) :- N is X*Y, palindrome(N), X1 is X-1, problem4(X1,X1,N,A).
problem4(X,Y,Z,A) :- Y1 is Y-1, problem4(X,Y1,Z,A).

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

*/

5.swi

problem5(Answer) :-
	flag(answer,_,1),
	forall(between(2,20,N),flag(answer,A,A*N//gcd(A,N))),
	flag(answer,Answer,Answer).

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

:- use_module(library(primes), [isPrime/1]).

problem7(Answer) :- findall(N,prime(N),L), last(L,Answer).

num(N,X) :- N = X; succ(N,N1), num(N1,X).

prime(N) :-
	flag(index,_,0),
	num(2,N), isPrime(N),
	flag(index,I,I+1),
	(I =< 10000 -> true; !, false).

8.swi

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

problem8(Answer) :- findall(N,prod(N),L), max_list(L,Answer).

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

tail([H|T],L) :- L = [H|T]; tail(T,L).

num(N) :- data8(Data), member(L,Data), i2d(L,L1), member(N,L1).

data8([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, !.