A Prolog solution to the FiveThirtyEight island liars Riddler (2/22/19)

liars.pl

% import our CLP library for constraint declarations
:- use_module(library(clpfd)).

% A Claimant is a liar if their age is over the threshold. We also
% explicitly declare the "not liar" condition here since `not` seems
% to behave weirdly with constraints
liar(Claimant, LieThreshold) :- Claimant #>= LieThreshold.
not_liar(Claimant, LieThreshold) :- Claimant #< LieThreshold.

% A Person is older than an Age if the Claimaint is not a liar, otherwise
% they are younger than or equal to that age
claim_older(Person, Age, Claimant, LieThreshold) :- 
	liar(Claimant, LieThreshold),
	Person #=< Age.
claim_older(Person, Age, Claimant, LieThreshold) :- 
	not_liar(Claimant, LieThreshold),
	Person #> Age.

claim_younger(Person, Age, Claimant, LieThreshold) :- 
	liar(Claimant, LieThreshold),
	Person #>= Age.
claim_younger(Person, Age, Claimant, LieThreshold) :- 
	not_liar(Claimant, LieThreshold),
	Person #< Age.

claim_equal(Person, Age, Claimant, LieThreshold) :-
	liar(Claimant, LieThreshold),
	Person #\= Age.
claim_equal(Person, Age, Claimant, LieThreshold) :-
	not_liar(Claimant, LieThreshold),
	Person #= Age.
	
claim_not_equal(Person, Age, Claimant, LieThreshold) :-
	liar(Claimant, LieThreshold),
	Person #= Age.
claim_not_equal(Person, Age, Claimant, LieThreshold) :-
	not_liar(Claimant, LieThreshold),
	Person #\= Age.

% Run this by giving a list of 5 islanders and an age threshold
% Example:
% ?- run([A, B, C, D, E], L).
run(Islanders, L) :-

	% Constrain our ages from 10 to 40 years old
	Islanders ins 10..40,
	L in 10..40,

	[A, B, C, D, E] = Islanders,

	% Claims from the original Riddler product statement
	claim_older(B, 20, A, L),
	claim_older(D, 16, A, L),
	claim_older(C, 18, B, L),
	claim_younger(E, 20, B, L),
	claim_younger(D, 22, C, L),
	claim_equal(A, 19, C, L),
	claim_not_equal(E, 17, D, L),
	claim_equal(B, 20, D, L),
	claim_older(A, 21, E, L),
	claim_younger(C, 18, E, L).