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Amusements in Mathematics

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
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.
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