Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."
In her Parade Magazine column of May 5, 1996, Marilyn discusses the following riddle:
In a meeting of all the native wives, a (male) missionary announces that at least one husband has been unfaithful. It is the tradition on that island that if a native wife discovers her husband has not been faithful, she would shoot him that midnight. Every native wife knew about the fidelity of every husband except her own, and never discussed her husband's fidelity with anyone else. After seven peaceful nights, shots were fired at midnight on the eight night. How many husbands were unfaithful?
Marilyn, assuming that all the native women have the same powers of logic that she does, correctly noted that if only one husband had been unfaithful, his wife would have immediately realized that, since no other husbands had been unfaithful, her husband must be guilty, and she would have shot him that first night at midnight. Therefore, any other wife, who knew of only one unfaithful husband, would immediately realize if he was not shot the first night at midnight, that her own husband must also be unfaithful, and both unfaithful husbands would be shot the second night at midnight. Similary, if a wife knew of any number n of unfaithful husbands, she would realize that if they were not shot on the nth night at midnight, that her own husband had been unfaithful, and the n+1 husbands would be shot on the n+1st night at midnight.
Therefore, there were eight unfaithful husbands.
After correctly solving the riddle, Marilyn then suggests that the unfaithful husbands could have postponed their day of reckoning by persuading the faithful husbands to join them, increasing the number of unfaithful husbands.
John Baskette email@example.com realized that the logical women populating this island surely would not have been fooled by the trickery you suggest. Such women would no doubt quickly calculate the night that the shootings would occur.
The women with faithful husbands know that if their own husband is faithful, that the shootings should occur on the eighth night. They know that if no shootings occur on the eighth night, it must be that their own husband is faithless. This will follow, no matter what the other husbands on the island do subsequently.
Similarly, the women with faithless husbands, who see only seven (other) faithless husbands will quickly calculate that if their own husbands are faithful then shootings should occur on the seventh day. If no shooting occurs on the seventh day, that means that their own husband must have been in the group of faithless husbands that the missionary saw before he left the island. The fact that other faithful husbands become faithless in subsequent days makes no difference.