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I was thinking about a piece that moves like gryphon after bouncing
I think the example diagram is incorrect. The Fox original diagram is : White : Ka3 Pf5 Ae8g1 Black : Kd5 Rb2d1 Nb8a5 Pa7a6f6c4g4c3g2 Ah5 There is a twin with b) Pa7->é2 The solution is a) 1.c2 Ab5 2.c3 Axg2# b) 1.g3 Axb8 2.Af3 Axf3# Both model mates.
This looks a bit like the QBall from <a href='http://users.actcom.co.il/~bruck/PartyChess.html'>Ackanomic's Party Chess</a>, except that the latter <em>must</em> bounce off the side.
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Here a piece I'm calling the Spinning RC Car that moves like a crooked Bishop after the bounce