261.--THE MONK AND THE BRIDGES.

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.

[Illustration]

Amusements in Mathematics · 第 294 / 970 题