Problem: Three Men In A Boat

A certain generous London manufacturer gives his workmen every year a week's holiday at the seaside at his own expense. One year fifteen of his men paid a visit to Herne Bay. On the morning of their departure from London they were addressed by their employer, who expressed the hope that they would have a very pleasant time.

"I have been given to understand," he added, "that some of you fellows are very fond of rowing, so I propose on this occasion to provide you with this recreation, and at the same time give you an amusing little puzzle to solve. During the seven days that you are at Herne Bay every one of you will go out every day at the same time for a row, but there must always be three men in a boat and no more. No two men may ever go out in a boat together more than once, and no man is allowed to go out twice in the same boat. If you can manage to do this, and use as few different boats as possible, you may charge the firm with the expense."

One of the men tells me that the experience he has gained in such matters soon enabled him to work out the answer to the entire satisfaction of themselves and their employer. But the amusing part of the thing is that they never really solved the little mystery. I find their method to have been quite incorrect, and I think it will amuse my readers to discover how the men should have been placed in the boats. As their names happen to have been Andrews, Baker, Carter, Danby, Edwards, Frith, Gay, Hart, Isaacs, Jackson, Kent, Lang, Mason, Napper, and Onslow, we can call them by their initials and write out the five groups for each of the seven days in the following simple way:

| 1 | 2 | 3 | 4 | 5 :------------- |:------------- |:------------- |:------------- |:------------- |:------------- | First Day:| (ABC)| (DEF)| (GHI)| (JKL)| (MNO)|

The men within each pair of brackets are here seen to be in the same boat, and therefore $A$ can never go out with $B$ or with $C$ again, and $C$ can never go out again with $B.$ The same applies to the other four boats. The figures show the number on the boat, so that $A, B,$ or $C,$ for example, can never go out in boat No. $1$ again.

Solutions: 1

Problems: 1
Solutions: 2

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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