[r-t] 3 and 4
Richard Smith
richard at ex-parrot.com
Mon Nov 29 18:51:05 UTC 2004
Samuel M. Austin wrote:
> How many different methods could be rung using 3 bells, not having more than
> 3 blows in one place and the method was to be say 18 changes long with no
> null changes?
I assume you also want the method to be true in the sense of
each row appearing three times? I also assume that you want
to include "methods" where each bell does something
different (e.g. Shipping Forcast). I have excluded
rotations, reflection, reversals and shorter method repeated
(e.g. Plain Hunt twice is not counted as a double-extent);
this leaves four extents:
&3.3.1.3.1.3.1.1.3,1 (3 blows) (PGR)
3.3.1.3.1.3.1.3.1.3.1.3.1.1.3.1.3.1 (3 blows) (R)
3.3.1.3.1.3.1.1.3.3.1.3.1.3.1.1.3.1 (3 blows) (R)
3.3.1.3.1.1 (x3) (3 blows) (R)
(The symbols in the final set of brackets are the methods'
symetries: P = palindromic, G = glide, R = rotational.)
> What would be the formula to work out the following question and how would
> it apply to 12, 24 and 30 changes?
It is unlikely that there will be a simple formula for this.
The figures are:
6 1
12 1
18 4
24 18
30 109
36 864
42 8720
> How many 48s of Minimus are there with not more than 6 blows in one place
> and no null changes?
Probably millions, going by the number of single extents --
see
http://www.math.ubc.ca/~holroyd/minimus.html
I don't have code to hand that will do this search in a
sensible length of time. If you want to restrict it
further, I might be able to give you an answer.
Richard
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