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Answer: 362880



In the purest form, the total number of changes in a peal is the factorial of the number of bells, representing ringing the bells in every possible order. According to "The Little Book of Bells" by Eric Hatch (Meredith Press, 1964), among other sources, the following have been given these names:


The higher numbers of these are theoretical. To expect bell ringers to maintain a pace of 2 or 3 rings every second, in never repeating and complicated patterns, for days or even weeks on end, is not physically possible. So they also use many of these words, including "caters", for smaller patterns that are actually possible to accomplish. But the answer required for a complete caters for the puzzle is 362880.

Posted by: Bob Lodge | Feb 3, 2004 7:41:54 PM

I was very confused by this. Most of the sources I found said that for more than 7 bells, a peal is perfectly and officially "correct" providing it has more than 5,000 changes and never repeats. I decided 9! was probably intended, but I really think the clue should have had the word "complete" in it somewhere.

Posted by: Adam Bliss | Feb 4, 2004 12:47:52 AM

I agree, Adam. I didn't stumble onto the existence of "partial" peals getting "full billing", so to speak, until too late. The words "correctly rung" are indeed weaker than "complete". I hope some of you enjoyed that nifty site with the animated change ringing.

Posted by: Bob Lodge | Feb 4, 2004 2:59:11 AM

This question caused me more trouble than it should have. I initially sent an e-mail to a bell ringer in England and asked him the question. He replied that 5,000 was the correct answer, so I penciled in 5,000 as my answer and then went to find a 2nd opinion.

Luckily, a clerk at a music store (who had never even heard of Peter Grimes or Old Joe) gave me the phone number of a bell ringer in his church who sometimes plays with the local symphony.

I called him and he was very nice to talk with. He gave me the correct answer of 9! and also took the time to explain why it was the correct answer. (As well as confirming my Brandenburg Concerto #5)

Posted by: Jeannette | Feb 4, 2004 7:21:14 AM

Thanks for that post, Jeanette. One of my greatest joys in proffering my puzzles is to imagine stymied young folks seeking answers from old timers, giving them a chance to share some special part of their life experience.

Posted by: Bob Lodge | Feb 6, 2004 7:41:39 PM

I emailed many experts and had differing answers. They assured me that peal meant ANYTHING over 5000. But I was prompted towards the 9! answer.

Posted by: Paula | Feb 8, 2004 6:33:25 PM

I also emailed several bell specialists in England who were all in agreement that the question was poorly worded - but they agreed 5000 should have been the best answer

Posted by: Mark | Feb 22, 2004 11:26:25 AM

Haha - there are probably bell-ringers all over the world who were wondering why they were being deluged with email ... I'm guilty as well ... but the question turned out to be more about mathematical possibilities than about bell-ringing.

At three rings a second, 9 factorial rings takes about 300 hours for you and a few friends ... any volunteers?

Posted by: Gneen | Feb 25, 2004 5:27:16 PM


The explanation of this clue in the May GAMES uses the phrase "5000 or fewer changes" where it should say "5000 or MORE changes". I noticed my goof and sent a correction to them, but it didn't make it into the last revision before printing.

Posted by: Bob Lodge | Mar 25, 2004 5:07:45 PM

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