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1. Rd6 Bg4
2. Rd2 Bf3
3. Bd3 Be4
4. Ra2#
But what if black responds 2… Be2? Then, it takes 5 moves! Hmmm. Must be missing something.
2… Be2
3. Be4 Bd3
4. Rd1+ Bb1
5. Rxb1#
OK. Here’s a better solution. Took a while to find.
1. Bh7 Bf1
2. Rh2 Bg2
3. Bd3 Be4
4. Ra2#
1… Bg2
2. Re6 Be4
3. Rxe4 Kb1
4. Re1#
How about…
1. Bh7 Bg2 2. Re6 Be4 3. Rxe4 Kb1 4. Re1
1. … Bf1 2. Rh2 Bg2 3.Bd3 Be4 4. Ra2
2. … Be2 3. Rh1+ Bf1 4.Rxf1
1. Rf6 Bg2 (only)
2. Rf2/Rf4 Bh3 (only)
3. Re2/Re4 any
4. Re1#
1.Bh7 Bf1 2.Rh2 Bg2 3.Bd3 B~ 4.Ra2#
1.Bh7 Bg2 2.Re6 Be4 3.Rxe4 Kb1 4.Re1#
Ouf, it took me a while and a board to join the anti-stalemate discovered double checkmate idea club
Pht, Rf6 doesn’t work because black can reply Bf5, blocking the white rook. Then, if Rxf5 or Bxf5, stalemate. White needs to move Bd1 to rescue his own bishop, after which white has insufficient time to mate black. It could go like this:
1. Rf6 Bf5
2. Bd1 Bh7
3. Rf2 Kb1
4. Bc2+? Bxc2
5. Rf1+ Bd1
6. Rxd1 Kc2
The black king is forking the white rook and pawn at c3 and has an escape route. At this point, white’s best option is Kb4 to let the black king take the rook and then promote the pawn on the c file. An easy win but far from mate in 4.
I can see that my first post was nonsence alltogether.
But I hope this one is not:
1. b4!
It simply has to be a pawn move!
This threats Kb3 and Ra6#.
1. … Bf1 (prevents both Ra6 and Rh1)
2. Kb3!
A timely zugzwang. It threats Ra6# directly when bishop moves. And now it becomes evident that next 2 moves mate:
2. … Bc4 (must stay in this diagonal)
3. Rh1+ Bf1
4. Rxf1#
The principle beeing that when rook threats mate both via a rank and via a file, then “the holy bishop” must be outmanouvered by zugzwang.
Oops, I’m afraid I missed that Kb3 Bc4 is check! Besides, b4 can be answered both with Bf1 and Bg2, making it unlikely that b4 is the solution. What a pity:-)
So it has to be a bishop move then to create threat in rank 2.
Bh7 seems to work fine, yes.
Pht, I like the 1. b4 move because it opens the a-file as an additional way to mate black, as you pointed out. It seems a strong move. However, the shortest line I could find from there was mate in five moves. And there was some zugzwang action in the various lines. For example,
1. b4 Bg2? (1… Bf1 2. c4 Bg2 3. Rd6 (3. Kb3 Bc6 4. Rd6 Ba4+ 5. Kc3 Ka2 6. Ra6 Ka3 7. Rxa4#) (3. b5 Bf1 4. Kb3 Bxc4+ 5. Kxc4 Ka2 6. Kc3 Ka3 7. Ra6#) (3. Ra6 Bb7 4. Ra5 Bc6 5. Kb3+ Ba4+ 6. Rxa4#) (3. Rg6 Bf1 4. Kb3 Bxc4+ 5. Kxc4 Ka2 6. Kc3 Ka3 7. Ra6#) 3… Bd5 4. Rg6 Bg2 5. Kb3 {Now the rook can mate at either g1 or a6.} Bc6 6. Rg1#) 2. Rg6 Bf1
3. c4 Bg2 4. Kb3 {Now the rook can mate at either g1 or a6, depending on black’s reply.} Bf1 5. Ra6#
Good puzzle, Anonymous has solved it!
Trying to solve it, I wondered if thinking what the pawns were doing might help. Actually, no! But, without the pawn on b3, there is mate in two, and without the pawn on c3, there are other mates in four – try it!