[r-t] parity

[Mark Davies]

Glenn Taylor writes,

> Faced with a CO of  265743 I don't *immediately* spot that
> it's out-of-course.

Depends on what you're used to, but for most people it'll work best with
5-figure COs. For 6-figure COs like you quote it's still pretty immediate
though - bring the 7 to the front with 3 shunts (negative) and the 5-figure
CO that's left (26543) is obviously positive. Hence -ve overall. That's
spottable in about a second or just under I reckon, which has to be an order
of magnitude quicker and easier than any other method.

The point is, if you do a bit of composing, or conducting (especially of LB
comps, which are primarily in-course) you've probably got a very good lookup
table in your head. A lookup table is a pretty fast way of solving the
problem, quickly, in your head, especially in conjuction with a device that
compresses the problem space, like the CO.

In general the algorithm works as follows:

1. Convert to CO.
2. If greater than 5* figure, remove bells one by one, keeping parity check.
3. Look up parity of remaining 5-figure CO.

* Or however large your personal lookup space is.

Obviously it'll work for rows as well as COs, and with the same lookup
table, but the problem space will be bigger hence more operations at step
(2).

I'm sure this is how most people actually do it, too...

MBD