An Eccentric Knight, introduced by me in some tours in Chessics #8 (p.10) 1979, always has one end of its move on an edge or centre cell of the board; the centre cells being d4, d5, e4, e5. If the 'or' is exclusive (i.e. not both to and from) the knight is confined to half the squares of the board, but if it is inclusive the edge-edge moves such as b1-a2 enable it to cover the whole board.
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Helpmate in 3.
Solution:1.Kh7 Kg5 2.Kh8 Kh6 3.Ng8 Ng6‡
This simple study shows paradoxical non-checks.
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Two problems, whole board for each.
White moves, then Serieshelpmate in 11 (left) or 9 (right).
I have a note that this was submitted to R. Turnbull, 8 November 1996, for Variant Chess.
Solution:
Left: Kb6 (still not in check) for 1-10.Kc4-d4-e5-e6-f7-e8-d8-c8-b8-a8 11.Sb8
and Sc7‡
Right: Sh4 for 1-8.Kh2-g3-f4-e5-e6-f7-g8-h8 9.Sg8 (not check) and Sg6‡ (Same mate as in previous problem)
Note: In the left diagram White is not in check, since the move d7-c5 does not involve an edge or centre cell.