Track Cheaters

Logic Level 2

5 boys are running at a track meet, 4 of them cheated, and these four all lied.
Bill: William did not do it
Jonathan: Bill ate a pill.
Bob: I don't have any drugs, but I saw Jonathan sneak a pill.
William: I don't know who did it, but Bill and Bob are telling the truth.
Avery: I know that Bill didn't do it.
Who did not cheat?

William Jonathan Avery Bill Bob

Kadin Ward by Kadin Ward , 15, USA

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4 solutions

Saya Suka
Mar 18, 2021

Avery supported Bill who supported William who supported both Bill and Bob. These four must be all the liars and cheaters, so Jonathan must have been the sole innocent truth teller.

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Jordan Cahn
Mar 15, 2019

William cannot be telling the truth, since there can only be one truth-teller. This means that William cheated, so Bill must be lying. Therefore he also cheated, which means that Jonathan is telling the truth and did not cheat.

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Zhong Si Wei
Mar 15, 2019

Bill said that William did not cheat and therefore told the truth, but if Bill told the truth, there would be 2 truth-tellers, which is impossible since there can only be one person who told the truth as the rest all lied. Therefore, Bill lied. In fact, all the people who claimed that another person didn't cheat lied due to the same reasoning that there would be too many truth-tellers, therefore Bob, Avery and William all cheated as they claimed that another person did not cheat. Since Jonathan is the only person who did not state that another person did not cheat, he is telling the truth and therefore did not cheat.

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Kadin Ward
Mar 14, 2019

Joe did not lie

0 Helpful 0 Interesting 0 Brilliant 1 Confused

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