10+11. Matt in 3 Zügen
Here, castlings are mutually exclusive. To see this assume, by way
of contradiction, that both sides may castle. Then wQ and wQR have been
captured by bNs (together with the wQB) and wQf4 is the promoted wPf2
on c8 or b8. So that bl. caps f7xg6, b7xa6, e7xd6 consumed the 2 wNs
and the wBf1. There are now three cases:
- wPf2 promoted on c8. Then it went through d6xc7
before bl. could play e7xd6 and release his Bf8 and Rh8, so that the
wPf2 captured the bQ and both bNs to reach c7, and the wPg2 captured
the bR on light-squared h3. As a consequence, when bl. finally plays
e7xNd6 & f7xNg6, letting the Rf8 reach h3 for capture, wPg2 and then
bPb7 & bBc8 are still home and wh. has no tempo move (his Q and QR have
already been captured).
- wPf2 promoted on b8
- through c7xb8=Q. Then the wPf2 had to go through
d6xc7 and we can borrow from previous case to see that the capture
was c7xBb8. But then there is no way the Bf8 could have reached b8
with a wP already at c7.
- through b7-b8=Q. When we play n. b7-b8=Q, the
wPf2 has already captured 4 bl. units and the bPb7 is already on a6,
so that g2xh3 and f7xg6 already took place. The bBc8 must be on c8,
as the only possible shield between bKe8 and wQb8 so that the only
move for Bl. is n ... c7-c6 before Wh. removes his wQ. But then Bl.
has no last move because only n-1 ... c7-c6 could have been played
just before n. b7-b8=Q.
Mate in 3 is with 1. Qxd6!! (threat. 2. Rf1 & 3.
Rf8#) Bb7 2. O-O !! (not 2. Rf1 ??) forbidding the
now-illegal defense 2 ... O-O-O??, and allowing 3. Rf8#.
Solution by Philippe Schnoebelen