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The Washington Post Jan. 12, 1975 p. 227
The Toil of the Toll
Any number of bells from four to twelve, as we have noted, may be rung
in changes in the various available methods. The number of possible
changes is determined by the factorial of the number of “working”
bells—those that shift position in a ringing sequence during the
changes—as opposed to the “nonworking” if loudly heard tenor (deepest,
3,588-pound) bell, which, in the method Stedman Caters, is always the
last of the bells to ring in each change. Eight is the normal number of
working bells used on those rare occasions when the Cathedral band or a
visiting band, usually English, attempts a full peal—the changes
necessary to achieve every possible permutation among the working bells.
The 5,040 changes require 3 hours, 25 minutes to complete. To ring every
possible change on 10 bells would require 75 hours, a complete peal on
12 bells, 40 years.
Many a Christmas tree has before it four little figurines carrying signs
with a single letter on each, the four of them together spelling out
N-O-E-L. Most people seeing these figurines are tempted to rearrange
them to spell L-E-O-N or E-L-N-O or whatever. Using one method of
change-ringing (Bob Minimus) one discovers the following complete set of
permutations for four bells:
| NOEL |
ELNO
|
EONL
|
NLEO |
EOLN |
| ONLE |
ENLO |
OELN |
NLOE |
ONEL |
| OLNE |
NEOL |
OLEN |
LNEO |
ONEL |
| LOEN |
NELO |
LONE |
LENO |
NOLE |
| LEON |
ENOL |
LNOE |
ELON |
NOEL |

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