Syn Problem

Level 2

Four children are arguing over a broken toy. Ali says Barbara broke it. Barbara says Tyler broke it. Tyler and Hei-Lam say they do not know who broke it. Only the guilty child was lying. The child who broke the toy was?

Tyler Barbara Ali Hei-Lam Cannot be sure

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3 solutions

Gavin Lo
May 11, 2015

Consider all the choices. Only the guilty child is lying. If Hei-Lam broke it, Barbara and Ali would both be lying. If Tyler broke it, Ali would be lying. If Ali broke it, Barbara would be lying. If Barbara broke it, only she would be lying, therefore she broke it.

Saya Suka
Apr 13, 2021

"Only the guilty child was lying".

2 children are accusing 2 different children as guilty, so one of them must be lying (the phrase is 'guilty CHILD'). Therefore, Tyler and Hei-Lam are truthful when they said they didn't know whodunnit and must also be innocents. Barbara accused an innocent Tyler, so she must be lying and also the real culprit.

Tyler and Hei-Lam both cannot lie. Because only the child who broke the toy would lie. So, they were not the ones who broke the toy. It was Barbara who broke the toy. Because Barbara told Tyler broke the toy. But Tyler wasn't lying.

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