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File: PuzzlesThatSoundImpossible Not sure how many of these I'll collect: ********> width=45% * Someone pushes a thingy on a table. It travels 2 metres and falls off the edge, taking two seconds to do so. Does it have wheels? * Cards face down, Alice can swap two, the Evil Dictator names one, Bob must find it? ******** width=10% ******** width=45% * Alice puts arbitrary integers in boxes labelled 1, 2, 3, ... Bob can open all but finitely many, then needs to name the number in one of the unopened boxes. Can he do it with non-zero probability? * 100 prisoners with names in boxes ********<