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Amusements in Mathematics by Henry Ernest Dudeney
page 280 of 735 (38%)

Some few years ago I happened to read somewhere that Abnit Vandermonde,
a clever mathematician, who was born in 1736 and died in 1793, had
devoted a good deal of study to the question of knight's tours. Beyond
what may be gathered from a few fragmentary references, I am not aware
of the exact nature or results of his investigations, but one thing
attracted my attention, and that was the statement that he had proposed
the question of a tour of the knight over the six surfaces of a cube,
each surface being a chessboard. Whether he obtained a solution or not I
do not know, but I have never seen one published. So I at once set to
work to master this interesting problem. Perhaps the reader may like to
attempt it.


341.--THE FOUR FROGS.

[Illustration]

In the illustration we have eight toadstools, with white frogs on 1 and
3 and black frogs on 6 and 8. The puzzle is to move one frog at a time,
in any order, along one of the straight lines from toadstool to
toadstool, until they have exchanged places, the white frogs being left
on 6 and 8 and the black ones on 1 and 3. If you use four counters on a
simple diagram, you will find this quite easy, but it is a little more
puzzling to do it in only seven plays, any number of successive moves by
one frog counting as one play. Of course, more than one frog cannot be
on a toadstool at the same time.


342.--THE MANDARIN'S PUZZLE.
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