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George Duke wrote on Wed, Jan 25, 2012 04:29 PM UTC:
{*****Bonus question: What planet are you standing on watching a transit of Mars?*****} Add a few Grasshopper-styles. Problemists in their chief era 1900-1960 have others besides Equihopper but they are not easily locatable. Weaker Grasshopper I described in error unable to leap adjacently is now ROACH. Regular Grasshopper strengthened to stop either one or two beyond the one screen is PLAGUE. Rook passively and full Hopper ('full' means regardless where the screen is) orthogonally is already Cannon for 1000 years. So add for one related example, Queen passively and ContraGrasshopper actively as CICADA. Don't use general ''Butterfly'' because each individual species will be needed. Then MONARCH ButterFLY can be sequential piece-type, first as Commoner then as ContraGrasshopper able but not required to capture once or twice at each required leg end. BLACK SWALLOWTAIL, divergent but not sequential, is Rook passively like Cannon, and actively contingently Grasshopper if the capture square is dark and ContraHopper if the capture square is light. The list of new Grasshoppers is not exhaustive of course, but only inchoate or inexhaustible actually. A DOUBLE-SCREEN GRASSHOPPER-Plex, able to capture not by displacement but by adjacency up to four units all 8 directions from its chosen arrival square past the two required screens is WINDSHIELD WIPER. Any or all the above can be made bifurcating too upon encountering second screen. Since bifurcators number over 50, variously Colliding, Bouncing etc., that is a lot more piece-types than accountable. ________________________________________________________ How many ContraGrasshoppers are required to give mate? Two work in set-up like: White CG h1, CG h2, King f8; Black King h8. But is that attainable? Or instead does it take three ContraHoppers, or four ContraHoppers? Relatedly the problem How_Many_Mets? was followed by unresolved yet Rejoinder. xxx

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