A prolog program, swipl (it takes less than a second to solve your puzzle)

N is number of turns of don't know answers. the bad predicate means that the person can know its number at turn N.

  bad(_,_,_,-1) :- !,false.
  bad(_,A,A,0) :- !.
  bad(A,_,A,0) :- !.
  bad(A,A,_,0) :- !.
  bad(B,C,A,N) :- D is abs(B-A),D<C,N1 is N-1, bad(B,D,A,N1),!.
  bad(C,A,B,N) :- D is abs(B-A),D<C,N1 is N-1, bad(D,A,B,N1),!.
  bad(A,B,C,N) :- D is abs(B-A),D<C,N1 is N-1, bad(A,B,D,N1),!.
  
  solve(X,Y,Z) :- Y1 is X-1, between(1,Y1,Y),
                  between(0,2,N), Z is X-Y,bad(X,Y,Z,N).

  ?- solve(65,X,Y).
  X = 26,
  Y = 39 ;
  X = 39,  
  Y = 26 .