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Man and Beast 05: Punning by Numbers. Systematic naming of coprime triaxial oblique pieces.[All Comments] [Add Comment or Rating]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.
Yes, but do you want them expanded any further? Your previous comments on 3d Chess suggests not, but I would value confirmation of this.
When I expanded this page to maximum coordinate 8 I drew the line at 8:8:n leapers (n less than 8), but now I realise that I may have been making a mountain out of a forward-only 2:1:1 and 3:1:0 compound leaper (see above). The even-n ones are generated anyway by Man and Beast 07 rules as 8:8:2 Nrine, 8:8:4 Niltrap, and 8:8:6 Rhorolais, leaving only 4 odd-n ones, but filling this gap would require another chain of renamings like the 2009 one. The reason for this is that as well as all four SOLLs dividing by 4 with remainder 1, those of the 8:8:1, 8:8:5, and 8:8:7 hypotenuse pieces of the Fieldmouse/Flittermouse, Dieter/Dipper, and Broadwayman/10:3:3 leaper. Now there are already remainder-1 leapers with two of those first consonant/vowel combinations - the 8:7:4 Filcher and 8:6:3 Driberyl. Now Filcher could always go over to 8:8:1 and 8:7:4 become Pilferer to go with Prizemouse and Pipistrelle. Driberyl I'm stuck with, as it would require replacing Lyrebird for 10:3:0 qwith a bird neither ending with bird nor starting with an already-used combination. That leaves the option of changing the 7:1:1 Dieter, ideally with something equally contrasting with the 5:5:1 Feaster and 7:7:2 Dipper. The established Flamingo rules out Faster, but Slimmer would require only the removal of Isis, which so far appears to be used only as the name of a variant, not a piece in one. It occurred to me that I might get rid of the Ixion as well. This gave me the following plan of action: 1: Use Pilferer to free up Filcher. At the same time replace Molerat, as there is a bit of a gap between its SOLL of 49 and teh 43-45 of the other first-range rodent names. Thus: Filcher/Recoil => Pilferer/Plot Molerat/Secret => Sceptic/Doubt 2: Use the Molerat and another rodent name that I havetoyed with using - Hystrix, a kind of porcupine - for the non-square root-65 pieces, freeing up the Isis slot for Slimmer and getting rid of my coinage of Yramid (from Ledge, Pledge, and Pyramid). Thus: Isis/Pledge => Molerat/Secret Ixion/Yramid => Hystrix/Quill 3: Replace the Dieter-Dipper pair. The forward-only name remains equally applicable to Slimmer as to Dieter. Thus: Dieter/Lank => Slimmer/Lank Dipper/Eddie => Skimmer/Shave 4: Add in the 8:8:n ones, while also changing the FO Filcher's name to one based more on that rather than its Flincher predecessor. Thus: 8:8:1 Filcher/Fraud 8:8:5 Shirker/Skive 8:8:7 Obfuscator/Obstacle There are two flies in the ointment: I still haven't devised names either for the symmetric/FO 8:8:3 leapers (SOLL 137) or to replace Disparu for what will be Slimmer+Skimmer. If anyone had any idea I'll gladly read them. In the meantime I will go ahead with stages 1 and 2.
After much thought I have thought of a name for 8:8:3, by considering vowels followed by Q. I have now implemented: 1: Use Pilferer to free up Filcher. At the same time replace Molerat, as there is a bit of a gap between its SOLL of 49 and the 43-45 of the other first-range rodent names. This removes what I believe (excuse the pun) is the only deity name that I apply to a non-compound piece. Thus: Filcher/Recoil => Pilferer/Plot Molerat/Secret => Sceptic/Doubt As a side-effect I have cleared out the compounds Thirdmouse/Triad compounds Fictitious/Metcast, Primitive/Ptolemaist, and Tinpot/Tracery to free the endings (and perhaps some full names) for compounds of the new Filcher. I am now considering leaving Disparu in place, as it does have an S in it. I have taken similar liberties with Degu, Guru, Haiku. Kudu, Ormolu, Xanadu, and Zulu. That leaves the remaining stages as: 2: Use the Molerat and Hystrix for the non-square root-65 pieces, freeing up the Isis slot for Slimmer and getting rid of my coinage of Yramid (from Ledge, Pledge, and Pyramid). Thus: Isis/Pledge => Molerat/Secret Ixion/Yramid => Hystrix/Quill 3: Replace the Dieter-Dipper pair. The forward-only name remains equally applicable to Slimmer as to Dieter. Thus: Dieter/Lank => Slimmer/Lank Dipper/Eddie => Skimmer/Shave 4: Add in the 8:8:n ones, while also changing the FO Filcher's name to one based more on that rather than its Flincher predecessor. Thus: 8:8:1 Filcher/Fraud 8:8:3 Equivocator/Pause 8:8:5 Shirker/Skive 8:8:7 Obfuscator/Obstacle
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