integralof5y

Borges and Herbert Simons are two great minds, but their conversation is not deep since is mostly shared view about the meaning of human and machine intelligence. Today, with LLMs we have a tool to explore the relation between intelligence and language, between number of parameters, neural nets architectures and much more. So that conversation give us no new insight but is delightful to share time with such great people.

The five minutes phone call makes this claim dependent of duration. What happens when you allow 10 minutes time?

MECE seems to be just a mathematical partition, so it seems there is not need of a new term and acronym.

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 .