%- Read person saw number at position.
saw(alice, 1, 0).
saw(alice, 0, 1).
saw(alice, 0, 2).
saw(alice, 6, 3).

saw(bob, 1, 0).
saw(bob, 0, 1).
saw(bob, 1, 2).
saw(bob, 6, 3).

saw(dan, 1, 0).
saw(dan, 0, 1).
saw(dan, 2, 2).
saw(dan, 9, 3).

%- Consider the case when two people see one number and one person saw a anoth-
% er number. This doesnt actually mean the person "definitely" misread the nu-
% mber, but if the problem can be solved it measns they definitely did.
definitely_misread(Person, Digit, Position) :-
  saw(Person, Digit, Position),
  saw(Q, D, Position), Q == Person, D == Digit,
  saw(R, D, Position), R == Q, R == Person.

%- Read a person misread the digit at poisition at position.
misread(Person, Digit, Position) :-
  saw(Person, Digit, Position),
  not((definitely_misread(Person, D, P), D == Digit, P == Position)),
  (saw(Q, D1, Position), Q == Person, D1 == Digit),
  (saw(R, D2, Position), R == Q, R == Person, D2 == Digit).

%- Resolve if the question is actually the correct digit at that position.
correct(Digit, Position) :-
  (saw(alice, Digit, Position), not(misread(alice, Digit, Position)));
  (saw(bob, Digit, Position), not(misread(bob, Digit, Position)));
  (saw(dan, Digit, Position), not(misread(dan, Digit, Position))).

?- correct(D, P).
D = 1,
P = 0 ;
D = 0,
P = 1 ;
D = 6,
P = 3 ;
D = 1,
P = 0 ;
D = 0,
P = 1 ;
D = 6,
P = 3 ;
D = 1,
P = 0 ;
D = 0,
P = 1 ;
D = P, P = 2 ;
false.