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Naccel 2 squad reportback - exercise (a)
Posted By: Nack Ballard In Response To: Naccel 2 squad reportback - exercise (a) (Matt Ryder)
Date: Friday, 15 January 2010, at 9:31 p.m.
Nice job on (a), Matt. You didn't miss anything.
As you (belatedly) deduced, I referred only to six-syms within a quadrant field (the five points that don't include the Super); i.e., only the six-syms that are also squads. I did not intend to address larger, looser symmetries, which can, at the extreme, include positions like [roof, roof, S3, -4pt, -5pt, -5pt].
The good news for you is that while you worked harder than necessary on (a), tackling (b) should be more manageable. :)
I have included (though not part of (a)) clones -- identically shaped formations but slid over one point; these are listed on a second line when the name is the same. (Odds is a clone of Triple Split but I gave it a different name anyway as neither's fits the other.) The clones are still six-syms, though they don't reflect around the middle point of the field and their count therefore differs by 1 (or by 2, in one case).
I omitted high-field counterparts (e.g., [122223] is [544443] counted from the neighboring Super.)
Grouping them as you did by how far they are pushed away from the line of symmetry:
[333333] - Six-stack (sometimes just "Stack")
[222222]
[111111][233334] - Top hat
[122223]
[133335] - Maypole[223344] - Three-prime
[112233]
[113355] - Short odds
[123345] - Sombrero[222444] - Triple split
[111333] - Odds
[111555] - Triple wide[122445] - Feet out
[112455] - Feet in(Note: A "split" is the two-checker pair variant [42], and a "wide" is the pair variant [51].)
It should be noted that it is inefficient (though not useless) to learn special formations (symmetrical or especially otherwise) where one or more checkers occupy a Super (which is already so easy to count). If an integer count exists for a formation that includes Super(s), it always exists when you strip the Super checker(s) from the formation.
Learning formations that stray outside the field while skipping the Supers (i.e., leaving the Supers unoccupied) is more reasonable, but that is still not as efficient as learning field-confined squads, for two reasons:
(1) You can "hop" (move 6 pips or a multiple of 6 pips) the outsider(s) back into the field to create a learned squad (which is compact and easy to identify). (2) When checkers are in different fields, board symmetries such as relections and mirrors can be employed.
Nack
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