Mathematical_Recreations-Kraitchik-2e

Permutational Problems 219
The two husbands on the island
5,6 cross to the far shore and the DdEe··· abc ABC
wife then returns to the island.
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Two of the women on the is-
7,8
land cross to the far shore and DdEe···
the husband of the third returns
Cc AaBb
to the
island.
Since the boat is still at the island these last operations
may be repeated until just one couple is left on the near shore
and one on the island. These two couples may then be carried
to the farther shore by a final sequence of nine trips:
The husband on the island
1,2 fetches the husband on the n MmN Aa ...
near shore to the island.
The two husbands on the is-
3, 4 land go to the far shore and one n lm LMNAa···
wife there returns to the island.
A wife on the island fetches the
5,6 wife on the near shore to the - lmn LMNAa· ..
island.
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A wife on the island takes an-
7,8 other to the far shore and re- - mn NAa··.
turns.
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9
The two wives on the island go
to the far shore.
- - Aa···
Thus 9 + 8(n - 3) + 9 = 8(n - 1) + 2 = 8n - 6 trips are
required to transport the n couples.
There is a certain ambiguity in the problem owing to dif-