[r-t] Crambo - mystery solved(?)

[Alexander Holroyd]

Very impressive, Richard.  It _is_ possible on 6 (and I would guess on all 
higher numbers).  Here is an example (which I think it is safe to say 
no-one in their right mind would ring).

p = 234.345.234.45.234.345.234.45.234.345.234.5
- = 234.345.234.45.234.345.23.45.234.345.234.5

720:
1234
----
- 2
  3-
2  2
  2
3-3-
----

On Thu, 7 Sep 2006, Richard Smith wrote:

> Robert  Johnson wrote:
>
>> Here's a funny little question vaguely inspired by crambo
>> (tho' crambo doesn't actually have this property). Can you
>> constuct an extent on n which remains a legal touch if you
>> strike out any row.
>
> Other than the trivial solutions on 1 and 2 bells, it is not
> possible for n < 6.  The proof for n = 5 is quite involved
> because of the number of steps involved and cases to be
> considered.  I hope I haven't overlooked any possibilities.