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[FEN "8/8/4R3/8/2kBn3/K2pQ3/8/8 w - - 0 1"]

1. Re5?

With White to move, here is a mate in two problem that I couldn't figure out. My opinion is that the first move is 1. Re5, but Black still has a variety of moves. Does anyone have better ideas on how to solve it?

1
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With the rook on e6, Bb6 is mate in two. For instance

  1. Bb6 d2 2. Qb3 mate or 1. ... N any 2. Qc5 mate or 1. ... Kc3 2. Qc1 or 1. ... Kc5 2. Qxd3 or 1. ... Ke4 2. Qxe4
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  • Wow lichess doesn’t see it! A plus 1 for you! – fartgeek Dec 23 '20 at 18:13
  • @fartgeek Yeah, "Lichess" does see it, in the blink of an eye. – Mobeus Zoom Jun 12 at 14:49
  • @MobeusZoom not on depth 18… – fartgeek Jun 13 at 12:22
  • @fartgeek Doubt that's possible, depth 18 vs depth 25 makes no difference in spotting a #2. (It only changes eval 19+ moves down the line.) – Mobeus Zoom Jun 13 at 15:53
  • @MobeusZoom You are lacking a critical understanding in how search depth works. I recommend you peruse an article germane to this subject… – fartgeek Jun 13 at 23:58
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I think it is useful in these sorts of problems to categorize moves. You say that Re5 looks promising, but that there are too many moves for black afterwards. I would work through this as follows:

What's good about Re5? It prevents the opponent's king from moving, shrinking the possibilities we need to consider. The threat is 2. Rc5#, but this is prevented by black's knight. If knight moves, 2.Rc5# will be possible because there are no checks. If pawn moves Rc5# remains impossible and no other mate presents itself.

Note that I don't need to consider where the knight is moving to. Since we know our threat after Re5 all we have to consider are moves that prevent that threat from working. d2 is such a move, and tells us that Re5 doesn't work.

To find the correct solution, we need to find a different solution to 1... kb5 or kd5. Blocking with the rook of queen like you've proposed doesn't work, so we have to instead look for situations where those moves are mate in 1. This leads us to realize our bishop being in the way is a serious problem, which motivates 1. Bb6, which is indeed correct.

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