Mathematical_Recreations-Kraitchik-2e

CHAPTER NINE
PERMUTATIONAL PROBLEMS
1. DIFFICULT CROSSINGS
THERE are many problems of this sort. We shall treat a
number of characteristic cases, approximately in the order
of their difficulty.
1. THE WOLF, THE CABBAGE, AND THE GOAT. A boatman
must carry a wolf, a goat, and a cabbage across a river in a
boat so small that he can take only one at a time. Furthermore,
he must be on hand to keep the wolf from eating the
goat, and the goat from eating the cabbage. How shall he
do it?
The key to the solution is the goat - the only one that
cannot be left unguarded in the presence of either of the other
two. One solution is: The boatman (1) takes the goat over,
(2) comes back alone, (3) takes the cabbage over, (4) brings
back the goat, (5) takes the wolf over, (6) comes back alone,
(7) takes the goat over. Another solution is found by interchanging
the wolf and the cabbage.
This problem suggested to Aubry the following question:
How shall we place in line 3 hunters, 3 wolves, 3 goats, and
3 cabbages without disturbing the peace by having a hunter
next to a wolf, a wolf next to a goat, or a goat next to a cabbage,
and without creating rivalry by having 2 hunters, 2
wolves, 2 goats or 2 cabbages side by side? The solutions are:
wcwcwchghghg and g h g h g hew ewe w.
A similar problem, also due to Aubry, is the following:
Four families, each consisting of a man, his wife and their
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