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Falcon Hexagonal Chess. The Falcon into the Hexagonal world. (Cells: 121) [All Comments] [Add Comment or Rating]
George Duke wrote on 2007-09-14 UTC
[Taking exception to Gilman's 'never has a switching property' for a later Comment, let's start with basics:] With also ARS's indulgence, the colour changes get interesting in hexagonal. In squares the categories Slider, Leaper, and Multi-path are descriptive enough that we usually omit a colour-describing trailer. For example, a Dabbabah-Rider is understandably colour-bound. Most of us are content with using 'colourbound' for such as Bishop and Camel too. Easily understood. On the other hand, we hardly bother with 'colour-switching'...except Gilman. Now Knight is 'colour-switching', an informative description, in that each successive move alternates White to Black, and we would like to preserve the quality and integrity of the definitions from squares to hexes. First, in hexes new adjective 'colour-changing' we propose for a (mandatory) move to either of the other 2 colours, as with Glinski-FHC Knight and Falcon both. By their three-colour alternations they can reach every square, a desideratum for design. Please refer to the extended definition of 'colour-changing' in our earlier Comment. The famous problem theme of Knight Tour and Falcon Tour becomes possible when all squares and/or hexes can be reached. Are there 1000 possible Knight tours on these 121 hexes? Are there 10,000 Falcon tours on ARS's 121? We have no idea immediately even an approximation the answer to this topic for research. ['Noncolourbound' also to be taken up separately]