Ringing the Changes

The Problem:

4 bells can be rung in several different orders - each sequence called a 'peal' .

Calling the bells A, B, C, and D, we have peals like : ABCD, ACDB, CADB etc.

'Ringing the changes' involves changing the order of the bells in a peal by a single 'swap' or 'exchange' of adjacent bells -

for example A B C D could become B A C D , using a Left exchange,

or A C B D , using a Middle exchange,

or, finally, A B D C , using a Right exchange .

The problem is to work your way through all the different peals, once and once only, using only L, M or R exchanges, and finishing up back at A B C D .

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Last modified: June 18, 2007