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This problem can be easily solved by using a simple diagram:
Each L represents a liar, & each T represents the man telling the truth.
These are the only three possible permutations for the scenario given. The
second permutation is actually not possible, because both A & C's statements
cannot both be lies, as A cannot be both guilty & innocent. The first
possibility makes B guilty, & the last possibility makes A guilty, so there
is a 50/50 chance that A or B is guilty, & C is definitely innocent.
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