/* File: Puzzles/ifthen.pro Author: If Then (sol MM)
Title: The false Statements
1. Only one of these statements is false
2. Only two of these statements is false
3. Only three of these statements is false
4. Only four of these statements is false
5. All five of these statements is false
Which if any is true?
?- start.
I = [false,false,false,true,false] ;
*/
start:- find(I),write(I).
/* mem/2: tests/generates if all the elements in the first list are
members in the second list.
| ?- mem([X,Y,Z],[a,b]).
X = Y = Z = a ;
X = Y = a ,Z = b ;
X = Z = a ,Y = b ;
X = a ,Y = Z = b ;
X = b ,Y = Z = a ;
X = Z = b ,Y = a ;
X = Y = b ,Z = a ;
X = Y = Z = b ; There are 2^3 = 8 solutions.
*/
mem([],L).
mem([H|T],L):- member(H,L),mem(T,L).
find([A1,A2,A3,A4,A5]) :- mem([A1,A2,A3,A4,A5],[true,false]),
Sol=[A1,A2,A3,A4,A5],
count(false,Sol,N),
((A1-> N=1 ) ; (not A1 -> not N=1)),
((A2-> N=2 ) ; (not A2 -> not N=2)),
((A3-> N=3 ) ; (not A3 -> not N=3)),
((A4-> N=4 ) ; (not A4 -> not N=4)),
((A5-> N=5 ) ; (not A5 -> not N=5)).
/* counts how many times an element (A) occurs in a list (first level)
?- count(b,[a,b,c,b],N).
N=2
*/
count(A,[],0).
count(A,[A|T],N):- count(A,T,N1),N is N1+1,!.
count(A,[_|T],N):- count(A,T,N).