Solution to Adultery Puzzle
If there was only one cheating husband, then on the day of the announcement, 999 wives would know there was one cheating husband, as they had already assumed; one wife, the one being cheated on, thought there were no cheaters, and now knows there is at least one. Hence, she realizes, it must be her husband who is cheating. So she turns him in.
Suppose instead there were two cheating husbands. On the first day, 998 wives know what’s up; wife #999 knows that husband #1000 is cheating, and wife #1000 knows that husband #999 is cheating. They both expect the one cheating husband to be executed. But neither one turns in their own husband, so nothing actually happens. Thus, after the executioner gets no offers, both wives realize that the only explanation is that there must be two cheating husbands, not one. So on day 2 there is a double execution. Reasoning this way, for our original problem, on the 50th day, all 50 cheated wives realize that their own husband is a cheater, and all 50 husbands get the chop.—