n dining not wisely but too well at a
certain London restaurant. They were the last to leave, but not one man
was in a condition to identify his own hat. Now, considering that they
took their hats at random, what are the chances that every man took a
hat that did not belong to him?"

"The first thing," said Mr. Waterson, "is to see in how many different
ways the eight hats could be taken."

"That is quite easy," Mr. Stubbs explained. "Multiply together the
numbers, 1, 2, 3, 4, 5, 6, 7, and 8. Let me see--half a minute--yes;
there are 40,320 different ways."

"Now all you've got to do is to see in how many of these cases no man
has his own hat," said Mr. Waterson.

"Thank you, I'm not taking any," said Mr. Packhurst. "I don't envy the
man who attempts the task of writing out all those forty-thousand-odd
cases and then picking out the ones he wants."

They all agreed that life is not long enough for that sort of amusement;
and as nobody saw any other way of getting at the answer, the matter was
postponed indefinitely. Can you solve the puzzle?

268.--THE PEAL OF BELLS.

A correspondent, who is apparently much interested in campanology, asks
me how he is to construct what he calls a "true and correct" peal for
four bells. He says that every possible permutation of the four bells
must be rung once, and once only. He adds that no bell must move more
than one place at a time, that no bell must make more than two
successive strokes in either the first or the last place, and that the
last change must be able to pass into the first. These fantastic
conditions will be found to be observed in the little peal for three
bells, as follows:--

1 2 3
2 1 3
2 3 1
3 2 1
3 1 2
1 3 2

How are we to give him a correct solution for his four bells?

269.--THREE MEN IN A BOAT.

A certain generous London manufacturer gives his workmen every year a
week's holiday at the seaside at his own expense. One year fifteen of
his men paid a visit to Herne Bay. On the morning of their departure
from London they were addressed by their employer, who expressed the
hope that they would have a very pleasant time.

"I have been given to understand," he added, "that some of you fellows
are very fond of rowing, so I propose on this occasion to provide you
with this recreation, and at the same time give you an amusing little
puzzle to solve. During the seven days that you are at Herne Bay ever