[r-t] Numbers

[Philip Saddleton]

Samuel M. Austin said  on 14/12/2006 14:02:
> 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
>   
But 13440 x 6 = 80640

7 can be in 6 positions relative to 8, but half of these are the reverse 
of the other half, accounting for each row twice.

-- 
Regards
Philip
http://www.saddleton.freeuk.com/