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Amusements in Mathematics

In this case I give a rough plan of a river with an island and five bridges. On one side of
the river is a monastery, and on the other side is seen a monk in the foreground. Now, the
monk has decided that he will cross every bridge once, and only once, on his return to the
monastery. This is, of course, quite easy to do, but on the way he thought to himself, "I
wonder how many different routes there are from which I might have selected." Could
you have told him? That is the puzzle. Take your pencil and trace out a route that will
take you once over all the five bridges. Then trace out a second route, then a third, and
see if you can count all the variations. You will find that the difficulty is twofold: you
have to avoid dropping routes on the one hand and counting the same routes more than
once on the other.