Solving logical puzzle with negation and undefined aspects in Prolog

Assume this trivial logic puzzle which I have made up:

There are three boys, Fred, John and Max. No two of the boys have the same age. Max is older than John. Fred is not the oldest one. Question 1: Who is the oldest one? Question 2: What could be possible orderings by age?

Obviously, Max is the oldest one. And, from the given information the following two orderings are possible: Max,Fred,John and Max,John,Fred.

But, formulating this trivial logic puzzle in Prolog appeared to be surprisingly difficult (at least for me, as I am still learning Prolog). Particularly the statement "Fred is not the oldest one" caused me a lot of headache. While this restricts the solution space, it still leaves possibilities open with respect to whether Fred is older than John or not.

In the end, I came up with the following solution, which works with SWI Prolog if you issue the query ?- fromoldest(A,B,C).:

boys(Boys) :- Boys = [fred,john,max].

older(A,B,List) :-
    nth0(A_idx,List,A),
    nth0(B_idx,List,B),
    A_idx < B_idx.

fromoldest(A,B,C) :-
    boys(Boys),                 % there are three boys
    permutation(Boys,[A,B,C]),  % all of different age
    older(max,john,[A,B,C]),    % max is older than john
    dif(A,fred).                % fred is not the oldest

I would be glad to get feedback on this approach:

• Is this idiomatic Prolog or what constructs should be preferred?
• Are there more straightforward ways of solving this?
• What about performance (like, use of permutation)?

posted over 2 years ago

CC BY-NC-SA 4.0

2y ago

Dirk Herrmann‭

1387 reputation 1 31 141 48