# Solution

(related to Problem: The Peal Of Bells)

The bells should be rung as follows:—

$$\begin{array}{cccc}1&2&3&4\\ 2&1&4 &3\\ 2&4&1 &3\\ 4&2&3 &1\\ 4&3& 2 &1\\ 3&4& 1 &2\\ 3&1& 4 &2\\ 1&3& 2 &4\\ 3&1& 2 &4\\ 1&3& 4 &2\\ 1&4& 3 &2\\ 4&1& 2 &3\\ 4&2&1 &3\\ 2&4&3 &1\\ 2&3& 4 &1\\ 3&2&1 &4\\ 2&3&1& 4\\ 3&2&4 &1\\ 3&4& 2 &1\\ 4&3& 1 &2\\ 4&1&3 &2\\ 1&4&2 &3\\ 1&2&4 &3\\ 2 &1&3 &4\\ \end{array}$$

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.

Thank you to the contributors under CC BY-SA 4.0!

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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