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MatPlus.Net Forum Promenade Monochromatic chess
 
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(1) Posted by Siegfried Hornecker [Sunday, Oct 4, 2020 22:12]

Monochromatic chess


I can't believe there's no thread about monochromatic chess yet. It has a lot of potential for composing, but probably everything has already been composed (if not earlier, then by Raymond Smullyan)

(= 6+9 )

SH, original (probably anticipated in idea - also note that this is NOT economical :-) )
White has additional pieces on g3, g5 and h6. What are those pieces?


(Monochromatic chess: No piece on a white square might end its move on a black square and vice versa)
 
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(2) Posted by Rosie Fay [Monday, Oct 5, 2020 10:48]

g3, g5 and h6 are all black. White's [Bc1] and [Ng1] never moved. White's other missing black-squared units are [Ra1], K and [Ph2]

A rook cannot change the parity of its rank-number, so h6 cannot be [Ra1]

For wK to move, White castled kingside.

If [Ph2] is on g3, wK could not have escaped from the cage of g1 and h2. So [Ph2] is not on g3.

Thus [Ph2] is on g5 (having captured there) or h6 (having captured on g5 and h6).

wK has never been on h6, as bNg8 has always guarded h6. (Never mind bBe3 and bRh4!)

If wK is on g5, it would be in an impossible double check from bQe5 and bBe3.

This leaves one possibility. Kg3 Rg5 Ph6. gxh6 cannot possibly be a capture of a black-squared unit, because the only candidate is [Pa7] This would've had to promote, which entails capturing 4 units, but there are not enough missing White units. And it wouldn't have been able to reach rank 2 anyway. Therefore gxh6 was the ep capture of [Ph7]

Valladao (White 0-0, White gxh6 ep and the need to rule out [bPa7] promoting in order to explain how come [Ph2] reached h6.)

Thanks for the problem.
 
 
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(3) Posted by Siegfried Hornecker [Monday, Oct 5, 2020 12:42]

You're a great solver! Congratulations!
(However, Pa7 has no path to promotion. So I guess I could have left one open... but then either Bc1 or Ke1 could get out without castling.)
 
 
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MatPlus.Net Forum Promenade Monochromatic chess