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# Bell Ringing

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Age 11 to 14

Challenge Level

- Problem
- Student Solutions

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?