2024/11/10 DPA: "Illusory Prevention"

Black to move:

Black is down 2 pieces so this is likely a checkmate puzzle.

A Ladder Mate with 2 Rooks is not possible when the King is within attacking distance of one of the Rooks.  But the Knight will support one of the Rooks.

1. ... Nf2+ is nice because there is only one response in 2. Kd2.  But 2. ... Rd3+  3. Kc2 Re2+  4. Kc1 Rd1#.

Where can White vary?  3. Kc1 and 3. ... Re1+  4. Kb2 Re2+ allows 5. Ka3.

Similarly, 3. ... Rc8+ allows 4. Kb2.  I don't think White can allow Black to reach b2.

We'd like to play ... Re2+ if the King is not on b2.

Also, if White gets to the f file, that looks bad for Black.

If White can't checkmate using the files, can he do it using the ranks?

The problem is the White Rook on a1, protecting the back rank.  But let's see.

1. ... Rd8+  2. Ke1 Re3+  3. Kf1 Nd2+  4. Kg1 and Black is out of checks.

1. ... Rd3+ gives White too many options.

1. ... Rd3+  2. Kc2 Rd2+  3. Kb1

1. ... Nf2^  2. Kd2 Rd3+  3. Kc1 Re2, threatening 4. ... Rd1#.

But this gives White time to defend:  4. b4 uncovers the Bishop to defend d1.

There is no way to block the b4 square so White can't push b4.

I had to pull out a board and start moving pieces since I can't visualize a solution.

I see it:  1. ... Nf2^  2. Kd2 Rd3+  3. Kc1 Re2  4. b4 Rd1+!!  5. Bxd1 Nd3+  6. Kb1 Rb2#.

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The key was seeing how 3. ... Re2 threatens checkmate and continuing to follow the line after 4. b4, which seemingly stops Black from playing ... Rd1+ but in fact does nothing of the sort, although the checkmate takes a different form, from a Ladder Mate to a semi-Smothered.

Another key is figuring out that, because of 4. ... Rd1+, the d3 square is now free for the Knight.

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One weakness of mine is discarding an idea too soon.  This would manifest itself by dismissing 3. ... Re2 because of 4. b4.  What I've been working on is to keep the idea and to re-introduce it at a later point or to simply continue analyzing it even though it looks like it fails.

In this case, the original idea of 4. ... Rd1# is prevented by 4. b4 but another checkmate now presents itself.  But one must be flexible in thinking or else one might miss the opportunity.

Another weakness is not recognizing that, because of a move, the board position has changed and, for example, a square has been freed up.  If one analyzed 4. ... Rd1+ only from the standpoint of the Bishop capturing the Rook, one would have missed the d3 square opening up.