I was not able to see the complete line to mate, but this should be the key idea for a black win.

If I had been playing black and white answered with 31. g3, then I might have played 31...Qf5. But probably I would have played 31...Nxf2+, followed by 32. Kg2 Nh4+ 33. Kxf2 Qf5+ 34. Ke1 Ng2+ 35. Ke2 Qf3#. (The last two moves can be played in reverse order.)

If instead white plays 33. Kg1, then black wins with 33...Nh3+ 34. Kh1 Qf5, and now white cannot stop ...Qf2 or ...Qf3 with mate to follow.

Yeah, BlazingArrow56 - After 39. Kg2 Ng4+ below:

Tough not to notice that the black knight on f3 is under attack. Should it be moved? Nope, instead

30...Ng4

threatens 31...Nxf2#. Taking the knight on f3 doesn't change this. White has only two ways of dealing with the mate threat (31 Qc2 and 31 g3), and one of them loses quickly. White needs to play

31 g3

because 31 Qc2 loses to 31...Rd2. This move attacks the queen and blocks the defence of f2. Capturing the rook with the knight allows the smothered mate.

Now, what does black play? A chess friend and I looked at the position and liked

31...N4xh2

seeing stuff like 32 Nxh2 Nxh2 33 Kxh2 Rd2, but then we peeked at the solution and saw that we weren't even close. I was also concerned that in many of these lines white could play moves like Qc3 with serious threats.

I think I can give myself the point.>

Here's my computer checked analysis:

<30...Ng4!! 31. g3>

The point of 30...Ng4!! is that White cannot play 31. gxf3?? Nxf2#, and this mate threat allows Black two aggressively positioned Knights and a tempo to initiate a winning attack against the now decisively weakened King position.

<31... Qf5!>

Also winning for Black is 31... Nxf2+!! 32. Kg2 Qf5 33. Be2 Rd2! 34. Qc3 (34.Nxd2? Qh3+ 35. Kxf2 Qxh2+ 36. Kf1 Qg1#) 34... Be5 .

<32. Be2>

Also losing for White is 32. Qc2 h4 33. Qe2 Ngxh2! (with the decisive threat 34. Nxh2 Qh3 ).

<32... Rd2! 33. Ra8>

Allowing Black a quick mate-in-four is 33. Nxd2? Nxf2+ 34. Kg2 Qh3+ 35. Kxf2 Qxh2+ 36. Kf1 Qg1#.

<33... Nxf2+!> This initiates a mate-in-nine combination.

<34. Kg2 Ne1+ 35. Kg1 Nh3+ 36. Kh1 Qxf1+!> The Queen sacrifice initiates a mate-in-six and is the only clearly winning move.

<37. Bxf1 Nf2+ 38. Kg1 Nf3+> 0-1

White resigns in the face of the coming mate-in-three, 39. Kg2 Ng4+ 40. Be2 Rxe2+ 41. Kf1 Rf2#.

Material: N+P for B. The White Kh1 has no legal move and is still potentially vulnerable to back-rank mates. Both sides have very active pieces. On one hand, Black has focused pressure on Ph2, from Bb8 (obscured by Rd6) and Nf3. The Black Nf6 and Qg5 can both join the K-side attack immediately. The Rd6 has an open file but is presently passive, because it defends Nf6. On the other hand, the White Qb3 and Bc4 form a battery attacking and pinning Pf7 to Kg8 behind it. The Bb2 rakes the adjacent diagonal (ready to remove Nf6 without warning), and Ra1 is ready to enter the Black position along the open a-file. The only piece on the entire board restricted solely to passive defense is the White Nf1, which guards Ph2. The tactical situation is tense, with White threatening 31.Bxf7+ or perhaps 31.Ra8. The threat 31.gxf3 also requires tactical assessment, with the zwischenzug Bxf7+ held in mind.

Candidates (30…): Qxg2+, Ng5

30…Ng5 (threatening 31…Nxf2#)

Amusingly, on 31.gxf3, control of g1 shifts from Nf3 to Qg5, so the threat 31…Nxf2# still holds. White has 3 options: (1) play the zwischenzug 31.Bxf7+; (2) guard Pf2 with 31.Qc2; or (3) provide the flight square g2 to Kh1 with 31.g3.

(1) 31.Bxf7+ Kf8

and White is worse for defense than in the lines below, because Bf7 hangs.

(2) 31.Qc2 Rd2 (threatening 32…Nxf2 and 32…Rxc2)

32.Qxd2 Nxd2 (threatening 33…Nxc4)

33.Ra8 [Nxd2 Qh4] Qd8 34.Nxd2 Qc7 (threatening 35…Qxh2# and 35…Qb7)

(3) 31.g3 Nxf2+ 32.Kg2 Qf5 (threatening 33…Nh4+ 34…Qf3+ 35…Nh3#)

33.Be2 {Kxf2 Nd4+] [Bxf7+ Kf8] Rd2

(3.1) 34.Nxd2 Qh3+ 35.Kxf2 Qxh2+ 36.Kf1 Qg1#

(3.2) 34.Ra8 Ne1+ 35.Kg1 Nh3+ 36.Kh1 Qxf1+ 37.Bxf1 Rxh2#

Because I do not move the pieces, I had board blindness and forgot that Pg3 was still there in line (3.2), but the game mate follows the same idea.

I disagree, the game line might not be obvious to everyone - I reached 33...Nxf2+ quite rapidly relative to my analysis thereafter. (I certainly found sacrificing the Q with so much firepower available a subtle concept.) Checks are plentiful, so that Black can even chase the K right over to the Q-side (e.g., to a3, in one line I saw fit to calculate), before Black loses to the mate threat from Ra8.

Hey, Johnlspouge. Do you remember me - SuperPatzer77? I completely agree with your remark about DavidD's explanation. Black has to stop White's mating threat of 33. Ra8 with the Black Queen sacrifice by Zsuzsa Polgar.

Of course, we all take our hats off to Zsuzsa (Susan) Polgar for stopping White's mating threat of 33. Ra8 and for sacrificing the Black Queen. She demolishes the White Knight defending the h2 square with 36...Qxf1!!.

Johnlspouge, it's nice to hear from you. Take care, Johnlspouge.

Sure: Cubby Montalvo, with the weird (but thoroughly gentle and enjoyable) sense of humor. How could I forget you?

<Take care, Johnlspouge>

Always. In fact, I use exactly this parting phrase myself - because I never liked "Take it easy" :)

Well, we have fun analyzing the chess games especially the greatest chess players such as Garry Kasparov, Victor Korchnoi, the three Polgar sisters, Tigran Petrosian and Jose Capablanca.

I'm a Jose Capablanca and Judy Polgar fan.

I'm originally from New York. Now I'm a Hoosier - LOL.

Adios, Adieu, Addio & Adeus, Johnlspouge -- LOL

SuperPatzer77

Okay, <znprdx>, here is another "trail of bread crumbs":

33…Nxf2+ 34.Kg2 Qh3+

which is followed by a chase across the board

35.Kxf2 Rxe2+ 36.Kxe2 Qg2+ 37.Kd1 Qxf1+ 38.Kc2 Qe2+ 39.Kb1

leading - oh whoops - to a loss for Black.

If Zsuzsa Polgar had followed that trail from the (IMHO) obvious 34...Qh3+ instead of the (again, IMHO) subtle 34...Ne1+ leading eventually to the Q-sac, we would not be seeing this game as our Sunday puzzle.