THE PEAL OF BELLS.
(
Combination and Group Problems)
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?
Answer:
The bells should be rung as follows:--
1 2 3 4
2 1 4 3
2 4 1 3
4 2 3 1
4 3 2 1
3 4 1 2
3 1 4 2
1 3 2 4
3 1 2 4
1 3 4 2
1 4 3 2
4 1 2 3
4 2 1 3
2 4 3 1
2 3 4 1
3 2 1 4
2 3 1 4
3 2 4 1
3 4 2 1
4 3 1 2
4 1 3 2
1 4 2 3
1 2 4 3
2 1 3 4
I have constructed peals for five and six bells respectively, and a
solution is possible for any number of bells under the conditions
previously stated.
