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@yohanes yohanes/cheryl.pl
Last active Aug 29, 2015

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% to run it: swipl -g 'conclusion' -t halt -q -s cheryl.pl
% http://www.straitstimes.com/news/singapore/education/story/primary-5-maths-question-goes-viral-stumps-adults-20150413
unique(A) :- aggregate_all(count, A, M), M==1.
birthday_list(15, may).
birthday_list(16, may).
birthday_list(19, may).
birthday_list(29, may).
birthday_list(17, june).
birthday_list(18, june).
birthday_list(14, july).
birthday_list(16, july).
birthday_list(14, august).
birthday_list(15, august).
birthday_list(17, august).
% bernard date is one in the list
bernard_date(D):-
birthday_list(D, _).
% bernard knows cheryl birthday for sure if the date is unique
bernard_knows(D) :-
unique(bernard_date(D)).
% albert knows the month M
% albert will think that bernard might know if the month M contains a unique date
bernard_might_know(M):-
birthday_list(D, M),
bernard_knows(D).
% albert is sure that bernard doesn't know, so we can narrow down the possible dates
possible_birthday(D, M):- birthday_list(D, M),
not(bernard_knows(D)),
not(bernard_might_know(M)).
% bernard can make a conclusion based on the D that he knows
% it means that the date is unique to a particular month
bernard_conclusion(D):-
possible_birthday(D, _),
unique(possible_birthday(D, _)).
% albert knows the month M
% albert knows that bernard can make a conclusion for the date D in that month
albert_month(M):-
possible_birthday(D, M),
bernard_conclusion(D).
% because albert can also make a conclusion,
% so there must be only one unique month
albert_conclusion(M):-
possible_birthday(_, M),
unique(albert_month(M)).
% the final conclusion is the month from albert and date from bernard
birthday(D,M):-
possible_birthday(D, M),
albert_conclusion(M),
bernard_conclusion(D).
conclusion:-
setof([D, M], birthday(D,M), L),
length(L, N),N==1,
birthday(D, M),
write(D), write(' '), write(M), write('\n'), !.
conclusion:-
write('Can not make conclusion\n'),
setof([D, M], birthday(D, M), L), write('Possible answers:'), write(L), write('\n').
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