Plaskett's Puzzle

Solution to Plaskett's Puzzle

In our Puzzle #16 we told the story of the Brussels GM tournament in 1987, where British GM Jim Plaskett showed us a remarkable problem, which nobody was able to solve, except for Mikhail Tal, who looked at it for ten minutes, then went for a walk in the park and came back with the solution.

Let us first look at the problem. In order to make it more difficult to find the position in study database I had mirrored the diagram. Here is the correct form as shown to us by Plaskett. At the time nobody knew anything about the author (which was not Jim Plaskett).

White to play and win

We mentioned a few obvious things in the above position. White cannot promote the pawn because of the knight fork on f7. Moving the king allows Black to defend the queening square e8 and use his own superior forces to settle the game.

So White hat to take more drastic measures: 1.Nf6+ Kg7! 1...Kh8 2.d8Q+ is mate in three; and 1...Kg6 2.Bh5+ Kf5 3.d8Q wins, as there is the forking square f7 is defended by the bishop. 2.Nh5+ Kg6. 2...Kf7 would block the forking square and allow 3.d8Q. 3.Bc2+! Forcing Black to take the knight – a very difficult move for computers to find. 3…Kxh5 4.d8Q!! (allowing the fork) Nf7+ 5.Ke6 Nxd8+ 6.Kf5.

Aha, a mate net has been cast out! White is threatening 7.Bd1+ e2 8.Bxe2 mate. 6…e2 7.Be4. Threatening 8.Bf3#. Black has only one reasonable defence – underpromotion! 7…e1N 8.Bd5!! c2 9.Bc4 (threatening 10.Be2 with mate in two) 9…c1N 10.Bb5 (threatening 11.Be8 with mate in two) 10…Nc7 11.Ba4.

Look at this situation. Black has four knight (and a bishop), but cannot stop the lone white bishop from delivering mate in three moves, e.g. 11…Ne2 12.Bd1 Nf3 13.Bxe2 and 14.Bxf3 mate.

A beautiful, fascinating problem, praised by many readers (see feedback below). However we discovered a fairly serious difficulty in this study. Actually it was the same Jim Plaskett who drew our attention to the fact that in the meantime analysts had found that Black can draw by playing 4…Kg4 (instead of going for the queen with 4…Nf7+). A bit of computer analysis confirmed: this seems to destroy the study by preventing a white win.

So we started to search for the study, using Harold van den Heijden’s monumental Endgame Study Database 2000, which contains over 58,000 studies. There we found three versions of the problem. Apparently the author had found the error in the above version and had attempted to correct it. In one case the author had moved the white knight from g4 to g8, which does not solve the problem. In the other he has moved the black knight in the starting position from g5 to e5. This does not allow 4…Kg4, because after that it is Mate in 9 (as Fritz instantly announces: 5.Qh4+ Kf3 6.Kxe5 e2 7.Qf4+ Kg2 8.Be4+ Kg1 9.Qe3+ Kf1 10.Qf3+ Ke1 11.Bd3 Kd1 12.Qxe2+ Kc1 13.Qc2#. This is the version we give in our replay solution below.

hehe

I already posted this puzzle. But its great enough to warrant a second post.

Well, it is great to know that this puzzle had been posted previously, I just thought to post it with a more complete explanation of what the puzzle was about

It looked like Lichess's stockfish found the tactic immediately at first glance. But the analysis is running on the cloud, on much stronger computers. Also, cloud analysis stops before Bc2, and so the position is marked as losing, despite cloud analysis, since the depth is "only" 30. But an offline analysis engine wouldn't see this checkmate.

This is a video from GM Oleksiyenko in 2018. At the time he didn't know where the study came from and Stockfish was unable to see the win for White.

This puzzle appears from time to time in chess forums and people  kept spreading rumours that engines cant solve. 

Actually stockfish could solve it since about 5 years ago in about 1.5 hour afaik.

Stockfish 14 can solve as fast as  3 mins now.

https://en.wikipedia.org/wiki/Talk:Plaskett%27s_Puzzle

The study is flawed, as is well known[edit]
After 4...Kg4, the position may be a technical win for White but it is far from clear, and it's even possible (if not particlarly likely) that something has been missed and Black can somehow draw it. Whether or not it's a technical win isn't all that important because the composer had 4...Nf7+ in mind as the main line, with the zig-zagging bishop manoeuvre and eventual mate. The fact that 4...Kg4 is a much stronger defence and gives white no clear and obvious winning line is a serious flaw. MaxBrowne (talk) 17:19, 5 April 2017 (UTC)

The puzzle position setup is probably incorrect, I think if we add a White pawn to h3 the starting position will be correct and allow the 14 move mate. I need time to run this on my computer. Currently, in the position being used with perfect play on both sides mate take 39 moves. IQ125 (talk) 17:37, 5 April 2017 (UTC)
If it interests you you are welcome to try things out with an engine, however the result of such research cannot be included in wikipedia. Only analysis published in reliable sources can be used. MaxBrowne (talk) 17:42, 5 April 2017 (UTC)
MaxBrowne hit the point. The puzzle says "White to play and win". Black has no choice for the first three moves. But for the fourth move, there is a choice, and the solution only covers 4... Nf7+. Moves 4.... Kg4 and 4.... c4+ for example are not covered. The puzzle solution must prove the suggested, "White to play and win", and this is not the case. Either "White to play and win" is correct, but then the flaw is, that this is not in the solution. Or it is incorrect; then the puzzle is not valid at all. Further, per my opinion, engine results regarding mate positions are valid. Some users can check them. But how to reference such engine results? Does somebody have a suggestion for this situation? Dlb (talk) 13:15, 17 June 2020 (UTC)
The puzzle is often referred to as a position, the engines can't solve (Grandmasters and Engines Couldn't Solve This Puzzle. Then Came The Magician on YouTube). As long it's not proven that the position is a win for White, this does not hold. Dlb (talk) 08:29, 18 June 2020 (UTC)
Because of the link to the chessbase article we're able to include the claim that 4...Kg4 refutes the study as originally set. However doing your own home analysis, with or without an engine, is the very definition of original research and can't be used on wikipedia. The chessbase article is a good source and I'll incorporate some of that material into the article. MaxBrowne2 (talk) 08:47, 18 June 2020 (UTC)The ChessBase article does offer a correction along these lines from Roberto Balzan: add a White pawn on h2. Double sharp (talk) 12:51, 3 March 2021 (UTC)

Mate in 34 or faster[edit]
PV of search by Stockfish 10 with full set of 7-piece Syzygy done at 2019-04-23 by me[1]

[FEN "8/3P3k/n2K3p/2p3n1/1b4N1/2p1p1P1/8/3B4 w - - 0 1"]
[SetUp "1"]

1. Nf6+ Kg7 2. Nh5+ Kg6 3. Bc2+ Kxh5 4. d8=Q Kg4 5. Qf6 Kxg3 6. Qe5+ Kf2 7. Qf4+ Ke2 8. Qg4+ Kf2 9. Bd1 c4+ 10. Kd5 Bf8 11. Qe2+ Kg1 12. Qxe3+ Kg2 13. Kxc4 Nc5 14. Qe2+ Kg3 15. Qg4+ Kf2 16. Qf4+ Ke1 17. Qxf8 Kxd1 18. Qxc5 c2 19. Kd3 c1=N+ 20. Ke3 Ne4 21. Qd5+ Kc2 22. Qxe4+ Kc3 23. Qd4+ Kb3 24. Qd1+ Kc4 25. Qxc1+ Kd5 26. Qh1+ Ke5 27. Qh2+ Kd5 28. Qxh6 Kc5 29. Ke4 Kc4 30. Qc6+ Kb3 31. Kd3 Kb4 32. Qb6+ Ka3 33. Kc3 Ka2 34. Qb2# 1-0