Four colleagues were suspicious to have discovered a secret of the highest level of classified information by outwitting the military computers. At the hearing, they have been asked who discovered the secret. But the transcript of the hearing only shows four statements, one made by each of the suspects. We do not know (and may even doubt) whether the minute taker has recorded word-for-word what they said during the hearing. But suppose, the minute taker has truly captured (maybe unintentionally) the right logical essence in all their speaking. Thereafter, according to the documents, no one in the commission had any idea what to do with the statements of the hearing.
Would you have been able to find out who discovered the secret, based on these four recorded statements?
Atkins:
It's not true that if I'm lying, Stone is also lying or Yates has discovered the secret.
Evert:
It's a lie that if I'm not telling the truth, Atkins is telling the truth or Stone has not discovered the secret.
Yates:
It is not the case that if I'm lying, Atkins and Evert have discovered the secret.
Stone:
If I'm lying, then either Atkins is telling the truth or Evert is lying or Yates has not discovered the secret.
In order for A's statement to be true, the "If I'm lying..." conditional would have to be false, but to falsify that, A would have to be lying. So A's statement can't be true and must be false. So the "If I'm lying..." conditional is true, and indeed the antecedent is true so the consequent is also: either S is also lying or Y has discovered the secret.
By the same reasoning with E's statement, A is telling the truth or S has not discovered the secret. Well, A is not telling the truth, so S has not discovered the secret.
Same reasoning with Y's statement: A and E have discovered the secret.
If S is telling the truth, the rest of his statement doesn't really tell you anything. If he's lying than A is lying (we knew that already) and E is lying and Y has discovered the secret.
Bottom line:
I can tell that A and E have discovered the secret, and also Y has discovered the secret. S is the only one not to have discovered the secret.
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Posted by Charlie
on 2016-12-27 09:45:00 |
solution
