Given: One hundred men are sentenced to be hanged. Their warden decides to give them a sporting chance at being pardoned. He says to them: “Each man has their photograph lying face down on a table in a nearby room. Each man is invited to enter the room alone and to overturn half the photographs. If a man overturns his own photograph, he gets a gold star. Each man must leave the room as he found it. If every man gets a gold star then all will be pardoned; otherwise all will hang. You may confer among yourselves.”
Question: Were the men given a truly _sporting_ chance?
Notes: No trick language involved. Natural assumptions (one name per box, etc) apply. The only strictly non-mathematics part of the puzzle is what constitutes a _sporting_ chance. I will leave that up to the problem solver.
Hint: I have seen this presented with the men instead being numbered ‘1’ to ‘100’, with boxes containing each man’s number instead of photographs showing each man’s face, and (hint hint!) with the boxes themselves labeled ‘1’ to ‘100’. Enjoy!
Philosophical Instigations 