Suppose you are a bellringer holding a rope and you look around the church tower and see the faces of 3 friends, all about to start change ringing. To ring a 'round' each bell is rung in turn (123412341234....). The bells can be rung in any order and changing the order is known as a 'change'. As your bell goes round on its wheel you can slow it down, or speed it up, just a little but not much, so you can only change places in the ringing order with the bell just before you or just after you.

By these rules NRICH can at first change to RNICH but not to RINCH. What are the other orders of the letters of the word NRICH that can be obtained in just one change of this sort?

The following example shows very simple 'bell music' starting with a round and ending with a round of 4 bells, showing 8 of the 24 possible permutations, or orders.

1234
2143
2413
4231
4321
3412
3142
1324
1234

Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?