Unexpected Egg Paradox

Unexpected Egg Paradox

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Medium:  Paradox
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Release Message:  An egg is concealed in one of ten boxes. You will not be able to deduce which box it is in before you open the box and see it.
Description:  Imagine that you have before you ten boxes labeled from 1 to 10. While your back is turned, a friend conceals an egg in one of the boxes. You turn around. ñI want you to open these boxes one at a time,î your friend tells you, ñin serial order. Inside one of them I guarantee that you will find an unexpected egg. By ïunexpected' I mean that you will not be able to deduce which box it is in before you open the box and see it.î Assuming that your friend is absolutely trustworthy in all statements, can this prediction be fulfilled? Apparently not. Your friend obviously will not put the egg in box 10, because after you have found the first nine boxes empty you will be able to deduce with certainty that the egg is in the only remaining box. This would contradict your friend's statement. Box 10 is out. Now consider the situation that would arise if your friend were so foolish as to put the egg in box 9. You find the first eight boxes empty. Only 9 and 10 remain. The egg cannot be in box 10. Ergo it must be in 9. You open 9. Sure enough, there it is. Clearly it is an expected egg, and so your friend is again proved wrong. Box 9 is out. But now you have started on your inexorable slide into unreality. Box 8 can be ruled out by precisely the same logical argument, and similarly boxes 7, 6, 5, 4, 3, 2 and 1. Confident that all ten boxes are empty, you start to open them. What have we here in box 5? A totally unexpected egg! Your friend's prediction is fulfilled after all. Where did your reasoning go wrong?