Spoiler Inside: Solution to Puzzle | SelectShow |
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Call the statements A1, A2, B1, etc.
Assume A1 (is true). Then Don has the trophy, A2 (is true), B2, not C2. B1 is false (as Alice is the truthteller). C1 (since Don can not be the truthteller). Not D2 (since Don has the trophy). Not D1 is forced. This solution is consistent. Assume not A1. Then Alice, Bob, or Connie has the trophy. Assume further D2. Then Alice or Connie has the trophy, B2, not D1 (since D2), not C1, not B1 (since Don is the truthteller, Bob must lie) and therefore C2 so Connie has the trophy. Therefore, C2. Contradiction: this would mean there is no liar. This is not a solution. Assume further, instead, not D2. Therefore, Bob has the trophy, A2, not B2, C1, and finally, C2. Contradiction: this would mean there is no truthteller since everyone has been established as having lied. This is not a solution. Therefore, the solution is A1, A2, B2, not B2, C1, not C2, not D1, not D2. Alice is the truthteller, Don the liar, and Bob and Connie alternate. Don has the trophy. |