1997-01 Solution

This is an easy one. Let's first write it out in a manner which indicates what each person thinks (J = John, A = Alice, F = Frank). The first clue is that since A and F have claimed the opposite thing, they both can't be telling the truth, and they both can't be lying. So one of A or F is telling the truth. This means J must be lying (only ONE person can tell the truth, remember). If J is lying, then A has the sweets. If A has the sweets, then F is telling the truth and A is lying, and it's all consistent.

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