I imagine the correct move is 25 a6, threatening immediate mate. I haven't yet worked out a response to 25 ... b6, but I think I've refuted any other tries for Black, as follows:

25 ... ba and 25 ... b5 both allow mate in 2, starting 26 Rxa7.

25 ... Bc7 allows mate in 1.

25 ... Qc7/Qd7 lose the queen, because 26 RxQ renews the mate threat, giving White time to save his own queen.

I see a few reasonable tries starting 25 ... Rd7, but they all leave White ahead in material:

25 ... Rd7
26 Rxd7 Nxc2
27 Rxd6 Bxd6
28 Bxg8

25 ... Rd7
26 Rxd7 Qxd7
27 ab+ Qxb7
28 Qg2

25 ... Rd7
26 Rxd7 Qxd7
27 ab+ Kxb7
28 Rxa7+ Bxa7
29 Qxa7+ Kc1
30 Qxd7+ Kxd7
31 Bxg8 (the point, although it seems that 30 Qa8+ is similarly good)

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25. Ba6 Rd7 (else mate) 26. Qf5 Rgd8 27. Bc5 Rxf7 28. Rxf7 Qc7 and here I found no way to win this immediately.

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Missed 25. Qb6!! because I didn't even consider the Queen sacrifice without a capture, even though quiet piece sacrifices have been a theme for our Chess puzzles this past week.

However, after missing 25. Qb6!! and looking at the game, I did have an insightful moment when I calculated 25... axb6 26. axb6+ Ba7 27.Rxa7+ Kb8 28. Rfxb7+ Kc8 29. Ba6! (diagram below):

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I don't see how to proceed after

25 a6 b6,

since the sacrifices at a7 and b6 don't seem to work. As for alternate 25th moves,

25 Ba6 seems to be defended by 25 ... Rd2, as per my 25 a6 line that depended on an eventual Bxg8.

25 Qb6 axb6
26 axb6+ Ba2

25. a6 b6 26.Qxb6 fails
25. Ba6, Rd7 gets nowhere
25. Qb6 Rd7 26.Rxd7 leaves the rook on g8 hanging... Time to check.

I did not see the gorgeous 26.Bc5! After that it was a bit of a mop up, except for 29.Bc5!

Black can put up more resistance with 27...Bxd6 28. Bxf7 axb6 29. axb6+ Kb8 30. Bxg8 Ng5 31.b4 - but who cares? Blacks busted. What a sweet game by Rubinstein! Brilliant!!

A buddy of mine was a nut for Rubinstein. Thought his anti-nimzo d4 systems were spectacular. A truly great player that sadly went tragically sick later in life.

It's immediately obvious that White will have to do something with his Queen, otherwise the Black Knight will take it next move. Also, although White has a better position than Black, it would be a pity if he lost his Bishop pair. That gets us to think of doing something drastic on the g1-a7 diagonal. Unfortunately, 25 Qxa7+ doesn't work. What about 25 Qb6, with the subsequent threat of Qxb7 mate? Then Black's candidate moves would be a7xQ, and Rd8-d7.

It took me some time to find the right order of moves for the first branch, but it eventually became clear that 25. Qb6 axb6 26. axb6+ Ba7 27. Rxa7+ Kb8 28. Rfxb7+ Kc8 29. Ba6 leads to mate, or huge loss of material, or both.

Then it was easy to see that after 25. Qb6 Rd7 26. Rxd7 Qxd7 27. Bxg8 axb6 28. axb6+ Ba7 29. Rxa7+ Kb8 30. Bc5 White is about a pawn better with a good position, so I got lazy and gave up the rest of the analysis. That was a pity, because while going through the other branches of the analysis tree Bc5 attacking the Queen had come up in several sub-variations. Oh, well!

By the way, here's what Stockfish has to say about my sub-optimal variation:

25. Qb6 Rd7 26. Rxd7 Qxd7 27. Bxg8 axb6 28. axb6+ Ba7 29. Rxa7+ Kb8 30. Bc5 Ng5 31. Ra1 Qg4 32. Bc4 Qf3 33. Kb3 Qf6 34. Kb4 Nh7 35. d4 exd4 36. cxd4 Qg6 37. e5 Ng5 38. Bd6+ Kc8 39. Ra8+ Kd7 40. Rb8 + (1.56--) Depth: 41/68 0:03:05 1285 MN

And here's Stockfish on best play for the combination (definitely non-human thinking on display after 30. BxRg8):

So today I got him to set up this POTD and together we tried to work through the position. He quickly spotted the black's Q+B fork and he also found the weakness on a7. With a bit more help we worked through the variations of Pa5 and Bc4 attacking Pb7. All the while I was racking my brains why none of them seemed to work. Not hoping to dampen his learning experience I was giving some such generalisations as

<"even though the obvious weakness is Pa7 the real weakness is Pb7, all we need to do is bring one more piece to bare on Pb7 and we can dominate the position">

<"all we have to do is work out which pieces can attack the king which is stuck in the corner and then work through each of those options until we find the best">.

I didn't find <Qb6> in the 10 minutes that we worked through the variations and he decided to look at the answer. Only after that did I realise that I had mainly missed the answer as I couldn't follow my own advice...

After 26.Ba6 Rd7 27. Qf5 Rgd8 28. Bc5 Rxf7 29. Qxf7 Qc7 30. Bc4 Qxf7 31. Bxf7 Bd6 32. Be3 white still holds advantage. Same after 26.a6 b6 27. Qe2 b5 28. Bb3

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Now black must lose material.

Beside the text solution black has two queen moves to consider. 26...Qg6 (for queen safety) loses to 27 Rxd7 with a forced mate.

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26...Qc7 (to exchange pieces) costs black a rook after 27 Qxc7 Rxc7 28 Rxc7 Bxc7.

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bug as b6 the key business at hand and rook foot in f7 coiled queen fudge d6 plod bishops aim c4 and g1,

ah jostle g8 etc and a7 targets a drive in f3 since,

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If ive got this correct recind be cuff re cutoff d7.

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see foil a d6 black at sixes and seens a gg you b6
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line of uncover batch in favour tactics a gone d5
knight also misses eg you manage to over see f4

after bishop g1 of course it is differ e7 in d6 suffers the sling bindings at gg get hup f7 rook in fastens too of a fashion in a cycle d6 crept in back door a b6 bind buff at b7 in sight a8.

25.Qb6 is a nice threat to consider.

25...axb6 26.axb6+ Ba7 27.Rxa7+ Kb8 28.Rfxb7+ Kc8 29.Ba6 seems too much to handle.

25...Rd7 26.Rxd7 Qxd7 27.Bxg8 axb6 28.axb6+ Ba7 29.Rxa7+ Kb8 30.Bc5 is not very convincing to me although I'm not sure it loses.

25.Qb6 would have to be a pretty gutsy move. What's wrong with the simpler 25.Qc5? 25...Nxg1 26.Qxd6 Rxd6 27.Rxg1 looks more solid.

B) 25.a6 b5
26.Rxa7+ Bxa7
27.Qxa7#

C) 25.a6 after Rd7 or b6, the attack stalls and White Queen is in danger. This gives the message that 25.a6 is wrong and perhaps Qb6 should be considered instead: D) 25.Qb6
<if....axb6 26.axb6+ Ba7 27.Qxb6 Qb8 28.Rxa7+ Qxa7 29.Qxa7#>

Analysis after 25.Qb6!!!:
25...axb6; Not the best. 25...Rd7 is better.
26.axb6+! Ba7; This is forced.
27.Rxa7+ Kb8; This is forced.
28.Rxb7+ Ka8; This is forced.
29.Ra7+ Kb8; SmallFish says White has a forced checkmate in 7 with best play.