# Retro Puzzle

Jun 22, 2009, 5:54 AM |
1
I like collecting bizarre chess problems and this is one of my favorites. It's more of a whodunit mystery than a chess problem.

Mate in 2.

Make no assumptions.  Everything should be proven :)

Note that the FEN string is intentionally incorrect in case you tried to cheat and peek at the FEN *grin)

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 ?" (See what I said about making no assumptions ...)

It cannot be proven that Black can't castle anymore. But it can be proven
that Black and White can't be both allowed to castle ... How????

Consider the Rook on d4. If it is the original Queen's Rook, then obviously White
can't castle anymore. If it is the original King's Rook, then the White King had to let it out of the bottom-right corner ... and he can't castle anymore.

You with me so far? It gets even better ...

Now, if it is a promoted Rook (kudos to you if you considered this as well), then it must have left the 8th rank by visiting square d8, or f8, or h8. In any case the Black King (or the black Rook) must have moved and Black can't castle anymore.

Finally, it can be proved that the two castlings (White's and Black's) are mutually
exclusive, but none may be proven impossible in itself. In other words, if one side castles, the other one CANNOT.

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.

Credit goes to Armand Lapierre who designed this puzzle a long while ago. I am yet to see a chess problem this unique.
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