[r-t] Gangnam

[Robin Woolley]

Hi All,

I only get digests, so apologies if this has been covered already.

What do I know? (I ignore variable hunt, half-lead singles - who knows, 
our band might like to ring an extent of Gangnam after I've got them 
through Rossendale).

1. Gangnam has non-trivial false leads:{163542,124536,165432, 125346, 
164352,(+123456)}

2. In an asymmetric method, these can be rung backwards to remove the 
falseness which results in the so-called Required Lead Heads, in this 
case: {23456, 24536, 25346, 63542, 64352, 65432} ~ S3

3. Gangnam is symmetric - so this method will not work because the 
trivial false lead of symmetric methods is the lead rung backward - the 
false row is still there. In fact, you will readily see that the 
false-lead set = required lead-head set.

Conclusion, a conventional extent is impossible.

To obtain a true 1440, we need to ring those changes around the 
half-lead with even parity, so we need to include odd-parity lead heads 
so this is why the conventional 720 works as Andrew Johnson pointed out.

As regards the 5040, what can we say? We can say 'the 5040 is true if 
the method has no non-trivial false leads' but is this 'iff'?

Best wishes
Robin