[r-t] Numbers

[Samuel M. Austin]

Afternoon, I've been thinking about extents of major with bells in their 
home position - some peals compositions have "6th the extent in 6ths" for 
example.

I've tried to come up with a simple formula for this and this is what I've 
got.

It may be completely wrong and it wouldn't surprise me if it is but here it 
is anyway and hope you don't mind looking at my working

Aye

Sam


Extent with 7-8 together

40320 / 3 = 13440

With 6,7,8 at home

40320 / (3 X 5) = 2688                     -   the 3 being the number 40320 
was divided by last  time               and the 5 the number of remaining 
bells

With 5,6,7,8 at home

40320 / (15 x 4) = 672

With 4,5,6,7,8 at home

40320 / (60 x 3) = 224

With 3,4,5,6,7,8 at home

40320 / (180 x 2) = 112

Also I have noticed that

112 X 2 = 224
224 X 3 = 672
672 x 4 = 2688
2688 x 5 = 13440

but then the rule changes

13440 x 3 = 40320

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