Mathematical_Recreations-Kraitchik-2e

Permutational Problems 221
Thus it takes 10 + 4(n - 4) + 11 = 4n + 5 trips to complete
the operation.
Tarry proposed a still further complication by adding to
the requirements made so far the assumption that one of the
husbands was a bigamist traveling with both his wives. The
problem can still be solved, but no fewer than 43 trips are
required for the transportation of 4 families.
4. THE THIEVES AND THE LOOT. Saint-Lague gave an
amusing problem of this sort:
Three robbers, old Babylas, his nephew Hilary, and Hilary's
son Sosthenes, stole a treasure chest from an old castle.
The treasure was hidden at the top of a tower overlooking a
river. To avoid pursuit they have had to destroy the ladders
by which they climbed up inside the tower, and their only
means of escape is to go down the outside of the tower by
means of a crude tackle they have with them. This consists
of a long rope with a basket at each end and a single pulley.
If the difference in weight of the contents of the two baskets
is greater than 20 pounds, the heavier basket descends too
rapidly for the safety of the robbers, though the box will
stand it. Babylas weighs 170 pounds, Hilary 100 pounds,
Sosthenes 80 pounds, and the treasure 60 pounds. But this
is not their only problem. When they reach the bottom they
divide the treasure into three unequal parts, the largest for
Babylas, and each puts his portion into a separate bag. They
must then cross the river in a boat so small that it will hold
only two men or one man and a bag. There is no honor
among them, and none of them wishes to leave his bag with
one of the others. However, they decide that the man who
is managing the boat will be too busy to tamper with the
bags. How did they make good their escape?
Solution: First they let the box down in one basket. When
that has reached the bottom Sosthenes climbs into the basket
at the top and goes down, bringing the treasure up. The box