[r-t] Bobs only Erin Triples (was: Composition search)

[Stephen Beckingham]

> I'm not sure what you mean by "six end" but being able to reduce the 
> number of comparisons sounds good :-)
> 
> -- 
> Alan Burlison

Hi Alan,
The "six end" is the change (row) at the end of the division of six changes. This can be any one of the 2520 in-course* rows. Within each division of six changes. If you examine a "six" you will see that the back bells fall into the same position 3 times, whilst the front bells rotate. Consider all the rows ending with 4567 - the 3 in-course rows all come in the same six....
132547631245673215476231456721354761234567
This six can be rotated to end with either 1234567, 2314567 or 3124567.
The other rows ending in 4567 are out-of-course, so occur at handstroke in the six ending in either 1235476, 2315476 or 3125476.
Therefore, as PABS says, the last 4 bells at the six-end uniquely identify the six.
It's an interesting problem - one that I have spent quite a lot of time on, with very little success.
Hope that helps
SJB

*rows that are an even number of swaps from rounds. In bobs-only erin, all the handstroke rows are out-of-course (an odd number of swaps from rounds) and all the backstroke rows are in-course. 		 	   		  
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