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George Duke wrote on 2009-07-16 UTC
Gilman goes along with problemists' Sexton for the shortest one of these (1,1,2). Its square of leap length is 6, and that prompts Gilman to pun many of the rest in naming. Presumably problemists all these decades did not turn to thinking about SOLL of 6 for Sexton, and their soundalike, because of limited treatment and also preoccupation with problems as puzzles for recreational math -- mates in 2, -3, helpmates, series-movers once they have a piece-type definition or mutator well liked. The method of exhaustion falls exclusively on Gilman's shoulders. 8^3 is 504 cubes, the maximum we should need. Recall from M&B01 chart, cubic Bishop has 2 bindings and Unicorn 4 bindings. Recall my recent comment at M&B04 having a demonstration proof, M&B04Comment28.June ,of cubic Ferz triangulating that uncovers further interesting correspondence. Namely, that in minimal 2x2x2, there are 48 Ferz triangulations out of 336 possible sequences; and the same numbers eerily correspond to 48 out of 336 from flat geometry for Falcon minimal-path three-steps out of all possible. The 336 in cubes is the same as saying 336 non-royal King moves possible within small manageable 2x2x2.

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