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Chess Geometry[Subject Thread] [Add Response]
Charles Gilman wrote on Sat, Nov 16, 2013 06:55 AM UTC:
I have a theory that every odd-SOLL leap on a hex board vcan be expressed as m diagnoal and n orthogonal steps at right angles in exactly one way, but cannot immediately see a way to prove it. Note that this is not the same as saying that every relevant SOLL can be expressed as 3m²+n² in exactly one way. For example, 49 is the SOLL of both the Heptagram (m=4, n=1) and the Settler (m=0, n=7) but as you can see, each has its own (unique) value of m and n. I have looked through several leapers without finding a counterexample. Does anyone know of either a counterexample or a proof of the theory?