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CROSSING
RIVER PROBLEMS
"My boat is on the shore."
BYRON.
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
fool.
Solution 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.
Solution 375.—FIVE
JEALOUS HUSBANDS.
During certain local floods five married couples found themselves surrounded
by water, and had to escape from their unpleasant position in a boat that would
only hold three persons at a time. Every husband was so jealous that he would
not allow his wife to be in the boat or on either bank with another man (or with
other men) unless he was himself present. Show the quickest way of getting these
five men and their wives across into safety.
Call the men A, B, C, D, E, and their respective wives a, b, c, d, e. To go
over and return counts as two crossings. No tricks such as ropes, swimming,
currents, etc., are permitted.
Solution 376.—THE
FOUR ELOPEMENTS.
Colonel B—— was a widower of a very taciturn disposition. His treatment of
his four daughters was unusually severe, almost cruel, and they not unnaturally
felt disposed to resent it. Being charming girls with every virtue and many
accomplishments, it is not surprising that each had a fond admirer. But the
father forbade the young men to call at his house, intercepted all letters, and
placed his daughters under stricter supervision than ever. But love, which
scorns locks and keys and garden walls, was equal to the occasion, and the four
youths conspired together and planned a general elopement.
At the foot of the tennis lawn at the bottom of the garden ran the silver
Thames, and one night, after the four girls had been safely conducted from a
dormitory window to terra firma, they all crept softly down to the bank
of the river, where a small boat belonging to the Colonel was moored. With this
they proposed to cross to the opposite side and make their way to a lane where
conveyances were waiting to carry them in their flight. Alas! here at the
water's brink their difficulties already began.
The young men were so extremely jealous that not one of them would allow his
prospective bride to remain at any time in the company of another man, or men,
unless he himself were present also. Now, the boat would only hold two persons,
though it could, of course, be rowed by one, and it seemed impossible that the
four couples would ever get across. But midway in the stream was a small island,
and this seemed to present a way out of the difficulty, because a person or
persons could be left there while the boat was rowed back or to the opposite
shore. If they had been prepared for their difficulty they could have easily
worked out a solution to the little poser at any other time. But they were now
so hurried and excited in their flight that the confusion they soon got into was
exceedingly amusing—or would have been to any one except themselves.
As a consequence they took twice as long and crossed the river twice as often
as was really necessary. Meanwhile, the Colonel, who was a very light sleeper,
thought he heard a splash of oars. He quickly raised the alarm among his
household, and the young ladies were found to be missing. Somebody was sent to
the police-station, and a number of officers soon aided in the pursuit of the
fugitives, who, in consequence of that delay in crossing the river, were quickly
overtaken. The four girls returned sadly to their homes, and afterwards broke
off their engagements in disgust.
For a considerable time it was a mystery how the party of eight managed to
cross the river in that little boat without any girl being ever left with a man,
unless her betrothed was also present. The favourite method is to take eight
counters or pieces of cardboard and mark them A, B, C, D, a, b, c, d, to
represent the four men and their prospective brides, and carry them from one
side of a table to the other in a matchbox (to represent the boat), a penny
being placed in the middle of the table as the island.
Readers are now asked to find the quickest method of getting the party across
the river. How many passages are necessary from land to land? By "land" is
understood either shore or island. Though the boat would not necessarily call at
the island every time of crossing, the possibility of its doing so must be
provided for. For example, it would not do for a man to be alone in the boat
(though it were understood that he intended merely to cross from one bank to the
opposite one) if there happened to be a girl alone on the island other than the
one to whom he was engaged.
Solution 377.—STEALING
THE CASTLE TREASURE.
The ingenious manner in which a box of treasure, consisting principally of
jewels and precious stones, was stolen from Gloomhurst Castle has been handed
down as a tradition in the De Gourney family. The thieves consisted of a man, a
youth, and a small boy, whose only mode of escape with the box of treasure was
by means of a high window. Outside the window was fixed a pulley, over which ran
a rope with a basket at each end. When one basket was on the ground the other
was at the window. The rope was so disposed that the persons in the basket could
neither help themselves by means of it nor receive help from others. In short,
the only way the baskets could be used was by placing a heavier weight in one
than in the other.
Now, the man weighed 195 lbs., the youth 105 lbs., the boy 90 lbs., and the
box of treasure 75 lbs. The weight in the descending basket could not exceed
that in the other by more than 15 lbs. without causing a descent so rapid as to
be most dangerous to a human being, though it would not injure the stolen
property. Only two persons, or one person and the treasure, could be placed in
the same basket at one time. How did they all manage to escape and take the box
of treasure with them?
The puzzle
is to find the shortest way of performing the feat, which in itself is not
difficult. Remember, a person cannot help himself by hanging on to the rope, the
only way being to go down "with a bump," with the weight in the other basket as
a counterpoise.
Solution
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