Each resident of Dot-Town carries a red or blue dot on his forehead, but if he ever figures out what colour it is, he kills himself. Each day, all the residents gather in the town hall and count the number of red and blue dots they see. However, they do not communicate their counts to one another. One day, a stranger comes and tells them something non-trivial about the number of blue dots. Prove that the aftermath of this event is that, eventually, every resident kills himself. [Note: Here, “non-trivial” means that there is some number of blue dots for which the statement would not have been true. Thus, through his statement, the stranger is effectively letting the residents of Dot-Town deduce a set K such that the number of blue dots cannot belong to K.]
Posted on: Thu, 05 Sep 2013 06:12:58 +0000
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