-1
$\begingroup$

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!


Each of Benny, Denny, Kenny and Lenny either always lies or always tells the truth.

  • Benny claims that Denny is a liar.
  • Lenny claims that Benny is a liar.
  • Kenny claims that both Benny and Denny are liars.
  • Kenny also claims that Lenny is a liar.

Which of them always lies and which of them always tells the truth?


This puzzle came from a Leningrad Mathematical Olympiad.

$\endgroup$
0

1 Answer 1

9
$\begingroup$

Ok, so this is the key understanding that made this make sense.

Kenny says that both of Benny and Denny are liars. Because of Benny's statement that Denny is a liar, Benny and Denny will always have opposite truth values. If Benny is True then Denny is False and vise versa.

Which means

Kenny must be a liar. Which means he is lying when he says that Lenny is a liar. Thus Lenny is telling the truth when he says that Benny is a liar.

Thus the final outcome is

Lenny and Denny are the two truth tellers, and Kenny and Benny are the two liars.

$\endgroup$
1
  • 2
    $\begingroup$ Welcome to PSE (Puzzling Stack Exchange)! $\endgroup$ Jan 30 at 20:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.