Three Culprits
17 Jun '12 16:451 editDonald finds that the delicious pie that was meant for the whole family has been eaten. He knows that one or more of the three rascals who live in his household are behind it, and that when confronted, the guilty one(s) will lie, and the innocent one(s) will speak the truth. The rascals tell him this:
Huey: Exactly one of us ate the pie.
Louie: Exactly two of us ate the pie.
Dewey: All three of us ate the pie.
Who ate the pie?
Far as I can tell, this problem has a unique solution. Does the apply for ten, as per the adjacent thread? How about a large number n?
Obviously n = 1 is impossible, as "exactly one" would implicate the person speaking, and if he ate the pie, he'd lie rather than confess. n = 2 has a clear solution though.
Huey: Exactly one of us ate the pie.
Louie: Exactly two of us ate the pie.
Dewey: All three of us ate the pie.
Who ate the pie?
Far as I can tell, this problem has a unique solution. Does the apply for ten, as per the adjacent thread? How about a large number n?
Obviously n = 1 is impossible, as "exactly one" would implicate the person speaking, and if he ate the pie, he'd lie rather than confess. n = 2 has a clear solution though.
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