All Jokers

Logic Level 3

The knight always tells the truth, the knave always lies, and the joker can either lie or tell the truth.

Ariel, Benedict, and Chris are a knight, a knave, and a joker. They make the following comments.

Ariel: I am a joker.
Benedict: Ariel is a joker.
Chris: Benedict is a joker.

Which of the following statements is true?

Ariel is the joker Benedict or Chris is the joker Any one of them could be the joker Chris is the joker Benedict is the joker Ariel or Benedict is the joker Ariel or Chris is the joker

View wiki
Chung Kevin by Chung Kevin , 45, Australia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Chung Kevin
Dec 28, 2016

Let's consider Ariel's statement. Only a Joker or a Knave can say that.

Case 1: Ariel is a Joker.
Then, Benedict is telling the truth, and so he must be the knight.
Then, Chris is telling a lie, and so he must be the knave.

Case 2: Ariel is a Knave.
Then, Benedict is telling a lie, and so he must be the joker.
Then, Chris is telling the truth, and so he must be the knight.

Thus, both cases are possible, and so we know that either Ariel or Benedict is the joker.

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Prince Loomba
Jan 2, 2017

Since we are required to find jokers, we will involve 3 cases.

  1. Ariel is joker: Ariel says truth, Benedict says truth and Chris lies. This can be possible when Benedict is knight and Chris is knave.

  2. Benedict is a joker: Ariel lies, Benedict lies, Chris says truth. This can also be possible when Ariel is knave and Chris is knight.

  3. Chris is a joker: Ariel lies, Benedict lies, Chris lies. Cant be possible as one of them is knight.

So Ariel or Benedict can be joker.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

When you say "This can be possible", you should also be explicit and show how it's possible, by saying which person has which role.

Calvin Lin Staff - 4 years, 5 months ago

Log in to reply

Mentioned the roles

Prince Loomba - 4 years, 5 months ago

I like how you solved this.

Chung Kevin - 4 years, 5 months ago

Log in to reply

Thanks very much!

Prince Loomba - 4 years, 5 months ago
Saya Suka
Feb 27, 2021

A Knight will only self-identify themselves as Knights (or indirectly as NOT a NOT-Knight), so Ariel obviously isn't one by her own words. Benedict or Chris must be the Knight, and respectively Ariel or Benedict must be the Joker.

Truth Values Ariel Benedict Chris
TTF Joker Knight knave
FFT knave Joker Knight
0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...