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Charles Gilman wrote on 2007-06-06 UTC
On reading 'Rooks and Knights are colourbound but Bishops are not' I
wondered why, and had a closer look at the moves. This drew other
anomalies to my attention - that the 'Bishop' had a move made of shorter
steps than the 'Rook' - so that two steps by a 'Bishop' in a straight
line, rather than a singler such step, equal two 'Rook' steps at an
angle. It occurred to me that it would make more sense to swap the names
round, call the 'Knight' a 'Camel', and reserve the term 'Knight'
for a piece leaping to the nearest cell not reachable by a Rook or Bishop
move. It's not as if there isn't room for another type of piece on this
many cells. That would then make the following statements true in this
geometry that are true on a square-cell board:
'The Rook and Knight are not colourbound - they can eventually reach any
cell on the board.'
'The Bishop and Camel are colourbound - they can reach only cells of the
same colour.'
'The Knight is colourswitching - it always start and ends a move on cells
of opposite colours.'
'The Knight leaps to the nearest cell not reachable by a Rook or Bishop
move.'
'The Camel leaps to the nearest same-colour cell not reachable by a Rook
or Bishop move.'
'A 2n-step move by a Crooked Bishop has the same destination as a 2n-step
move by a (straight) Rook.'
'A 3-step move by a Crooked Rook has the same destination as a Knight
leap.'
'A 3-step move by a Crooked Bishop has the same destination as a Camel
leap.'
I was going to add 'A 2n-step move by a Crooked Rook has the same
destination as an n-step move by a (straight) Bishop.' but on closer
investigation that's only for Crooked Rook steps through edges - through
vertices it's a 2n-step move by both. Even so, it's a lot closer to the
square-cell nomenclature.

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