[r-t] Grandsire Minor

[Alexander Holroyd]

On Sun, 17 Feb 2013, Richard Pullin wrote:

> On a similar wavelength, I'd be interested to know if anybody has ever
> come up with a 5040 of Grandsire Triples made up of five unjoinable
> bobs-only blocks. Or perhaps as the Q-sets are wholly In-Course in
> Triples, the anti bobs-only law doesn't allow events to get this
> 'near' to a bobs-only extent, unlike in Minor where the feature of the
> Q-set altering the nature of the rows can cause the added obstacle of
> needing to arrive in the blocks 'in the right direction'.

That isn't possible.  Any partition of the extent into mutually true 
in-course blocks of Grandsire Triples has an even number of blocks.  This 
was proved by W H Thompson in 1880 or so.  Professional mathematicians 
caught up with ringers in 1948 when Rankin published a formal proof of 
this and its natural generalizations.  This proof was simplified by Swan 
in 1999.

I guess this is what you are referring to as "the anti bobs-only law"!

RANKIN, RA. "A CAMPANOLOGICAL PROBLEM IN GROUP THEORY." Proceedings of the 
Cambridge Philosophical Society. Vol. 44. 1948.

Swan, Richard G. "A simple proof of Rankin's campanological theorem." The 
American mathematical monthly 106.2 (1999): 159-161.