Amusements in Mathematics
Crossing River Problems
"My boat is on the shore."
This is another mediæval class of puzzles. Probably the earliest example was by Abbot
Alcuin, who was born in Yorkshire in 735 and died at Tours in 804. And everybody
knows the story of the man with the wolf, goat, and basket of cabbages whose boat would
only take one of the three at a time with the man himself. His difficulties arose from his
being unable to leave the wolf alone with the goat, or the goat alone with the cabbages.
These puzzles were considered by Tartaglia and Bachet, and have been later investigated
by Lucas, De Fonteney, Delannoy, Tarry, and others. In the puzzles I give there will be
found one or two new conditions which add to the complexity somewhat. I also include a
pulley problem that practically involves the same principles.
373.—CROSSING THE STREAM.
During a country ramble Mr. and Mrs. Softleigh found themselves in a pretty little
dilemma. They had to cross a stream in a small boat which was capable of carrying only
150 lbs. weight. But Mr. Softleigh and his wife each weighed exactly 150 lbs., and each
of their sons weighed 75 lbs. And then there was the dog, who could not be induced on
any terms to swim. On the principle of "ladies first," they at once sent Mrs. Softleigh
over; but this was a stupid oversight, because she had to come back again with the boat,
so nothing was gained by that operation. How did they all succeed in getting across? The
reader will find it much easier than the Softleigh family did, for their greatest enemy
could not have truthfully called them a brilliant quartette—while the dog was a perfect
374.—CROSSING THE RIVER AXE.
Many years ago, in the days of the smuggler known as "Rob Roy of the West," a piratical
band buried on the coast of South Devon a quantity of treasure which was, of course,
abandoned by them in the usual inexplicable way. Some time afterwards its whereabouts
was discovered by three countrymen, who visited the spot one night and divided the spoil
between them, Giles taking treasure to the value of £800, Jasper £500 worth, and
Timothy £300 worth. In returning they had to cross the river Axe at a point where they
had left a small boat in readiness. Here, however, was a difficulty they had not
anticipated. The boat would only carry two men, or one man and a sack, and they had so
little confidence in one another that no person could be left alone on the land or in the
boat with more than his share of the spoil, though two persons (being a check on each
other) might be left with more than their shares. The puzzle is to show how they got over
the river in the fewest possible crossings, taking their treasure with them. No tricks, such
as ropes, "flying bridges," currents, swimming, or similar dodges, may be employed.
375.—FIVE JEALOUS HUSBANDS.