Spy problem

Logic Level 2

There are three peoples , Albert, Brad and Ken, one of whom is a knight, one a knave, and one a spy.

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

They are brought before a judge who wants to identify the spy.

Albert says: "I am not a spy."

Brad says: "I am a spy."

Now Ken is in fact the spy. The judge asks him: "Is Brad really a spy?"

What should Ken say so that he doesn't convict himself as a spy?

None of these No Yes

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Munem Shahriar
Jul 19, 2017

Ken should say '' No ''

Brad is either a knave or a spy. If Brad is a spy, then Albert is truthful and is therefore the knight.

  • Albert is a Knight

  • Brad is a Spy

  • Ken is a Knave

On the other hand, if Brad is the knave, there are two possibilities:

  • Albert is a Spy

  • Brad is a Knave

  • Ken is a Knight

or

  • Albert is a Knight

  • Brad is a Knave

  • Ken is a Spy

If Ken is either the knave or the knight, his answer to the question will be "No", and so the judge will not be able to draw a conclusion. On the other hand, Ken can say "Yes" only if he is the spy.

6 Helpful 1 Interesting 1 Brilliant 0 Confused

good explanation!

Mohammad Khaza - 3 years, 10 months ago

Exactly!!!!!!!!!!

Diana Bradish - 1 year, 1 month ago
Saya Suka
Apr 25, 2021

Albert : "I am not a spy."
✓ Albert is a Knight (True) or a Spy (False)

Brad : "I am a spy."
✓ Brad is a Spy (True) or a knave (False)

The above would be the possibilities that the judge can glean from the two statements from their POV as an outsider. In total, there should be 3 cases as listed in the table below.

Albert Brad Truth Values Ken
Knight Spy T & T knave
Spy knave F & F Knight
Knight knave T & F Spy

Ken's objective is to avoid detection, so he wouldn't want the last possibilities (which is actually the real case that we have here) to be realised by the judge, so he has to pretend to behave like a knave or a Knight in the first two cases.

The judge asks Ken about Brad spy status, and in both cases a supposedly knave Ken would lie with a "No" about a supposedly Spy Brad while a supposedly Knight Ken would have to tell the truth with a "No" about a supposedly knave Brad.

Sure, as a Spy Ken could also have answered "No" truthfully, but in the event that he accidentally made a mistake by choosing to lie, his "Yes" would be the end of him (as the unique answer from a Spy that will clue the judge in to the real truth)....

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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