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THREE MEN IN A BOAT.
(Combination and Group Problems
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.