"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?
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?