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.