This is an interesting logical reasoning problem written by martin gardner, a famous contemporary master of mathematical science. Mr. Tan, a mathematical science writer in China, introduced this interesting question in his book Wide Angle of Mathematics (published by Jiangsu Education Press 1998). Obviously, no one will shake hands with themselves or their spouses. Of course, two people don't shake hands. For various reasons, people who can shake hands do not always shake hands. So among them 10, the person who shakes hands the most can't shake hands more than 8 times. Mr. Wang has asked nine people to shake hands in different ways. So the number of times they shake hands should be 0, 65, 438+0, 2, 3, 4, 5, 6, 7 and 8 respectively. * * * Nine situations. Analysis shows that people who shake hands eight times and those who shake hands zero times must be lovers. This is because the person who shakes hands eight times may be assumed to be Mr. Zhang, and he must shake hands with all the four couples except Mrs. Zhang. Therefore, the number of handshakes of each of the four couples cannot be zero. Then, the person who shakes hands with Zero Time can only be Mrs. Zhang. So the number of handshakes between Mr. and Mrs. Zhang has been confirmed, so it is excluded ... So since the sum of handshakes is 8, it must be a couple, and no two of the nine people shake hands the same, so only Mr. Wang and Mrs. Wang shake hands the same.

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Mathematics for middle school students, 2 1, 2003