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Miscellaneous Problems

Solution

Armand Lapierre
Thèmes 64, Apr. 1959
4th Hon. Mention

[4k2r/p1p1p1p1/1p2P3/8/3R4/6P1/5P1P/R3K3]

7+7. Mate in 2

Solution: 1. Rad1 threatens 2. Rd8 mate and can only be defended by 1 ... O-O. So the question is "Is black O-O legal ?"

It cannot be proven that B can't castle anymore. But it can be proven that B and W can't be both allowed to castle:

Consider the R on d4. If it is the original QR, then obviously White can't castle anymore. If it is the original KR, then the wK had to let it out of the SE corner, and he can't castle anymore.

Now, if it is a promoted R, then it must have left the 8th rank by visiting square d8, or f8, or h8. In any case the bK (or the bKR) must have moved and B can't castle anymore.

Finally, it can be proved that the two castlings are mutually exclusive, but none may be proven impossible in itself.

Thus the try 1. Rad1?, threatening 2. Rd8 mate fails on 1 ... O-O! The solution is 1. O-O-O! and now 2. Rd8 mate can't be avoided because 1 ... O-O? is illegal.