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If the royal night is too easy to checkmate in my game design in the below comments, then it can be changed to an equus rex/crowned knight to give it the king moves in addition to the knight moves.
This is a fun and challenging chess variant. It would be nice if someone produced a 'KnightMate' specific set like the one shown in the below comments. I like the Mate the Knight concept and it might be interesting if there were a smaller variant played on a 6x5 board. The royal knights would be placed on c1 and c6, cardinals/archbishops on a1 and a6, and marshals on e1 and e6. The second row would consist of pawns that could move one square without en passant capturing. Pawn promotion would be for lost pieces, or, if no piece has been lost upon promotion, it becomes a non-royal knight.
White: Knight (d3) and Pawn (e7), Black: Knight (a6) and Rook (d8) +---+---+---+---+---+---+---+---+ 8 | |:::| |:r:| |:::| |:::| +---+---+---+---+---+---+---+---+ 7 |:::| |:::| |:P:| |:::| | +---+---+---+---+---+---+---+---+ 6 | n |:::| |:::| |:::| |:::| +---+---+---+---+---+---+---+---+ 5 |:::| |:::| |:::| |:::| | +---+---+---+---+---+---+---+---+ 4 | |:::| |:::| |:::| |:::| +---+---+---+---+---+---+---+---+ 3 |:::| |:::| N |:::| |:::| | +---+---+---+---+---+---+---+---+ 2 | |:::| |:::| |:::| |:::| +---+---+---+---+---+---+---+---+ 1 |:::| |:::| |:::| |:::| | +---+---+---+---+---+---+---+---+ a b c d e f g h
leads to 1.exd8(K) Nb8 2.Kc7 Na6 3.Kb7 mate! Promotion to a Queen is stalemate. To meet Robert's challenge in the first Comment, we need to verify that promotion to either Bishop or Rook in this position will also lead to a draw. This 'capture promotion' ending could reasonably happen in a real game after the Black Rook had captured on d8. But it would be extremely rare.
I ran end-game data-bases for this game, and it turns out that for the single-piece end-games only N+Q can force the royal Knight into checkmate. Not even a Rook suffices, and neither does a (Commoner) King. Any two-piece advantage can enforce checkmate, though, except N+N+N, but in Knightmate that is even outlandish as K+K+K in FIDE chess (but, by the way, easily beats K+R there!). In particular N+K+B is an easy win over a bare Knight, the position after b8(K) in the proposed problem is a mate in 10: 1. Kc7 Nb3 2. Nf3 Na5 3. Kb6+ Nc4 4. Bc5 Nb2 5. Kb5 Nd3 6. Be3 Nb2 7. Kb4 Nd1 8. Ba7 Nb2 9. Kc3+ Nd1 10. Kc2++
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