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An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information, or any number of logical impossibilities. 15 Puzzle – Slide fifteen numbered tiles into numerical order. Impossible for half of the starting positions. Five room puzzle – Cross each wall of a diagram exactly once with a continuous line.
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The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. Boolos' article includes multiple ways of solving the problem.