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A friend and I yesterday asked ourselves what the highest number of possible mates in a (legal) position is. We were able to come up with the following position which has a total of 76 unique mates in 1, but we then failed to improve upon this one.

Q3Q3/4K2Q/6R1/3R4/QB2k3/5R1N/2R5/QQ1Q1N1B w - - 0 1

Do you know if this problem ever has been solved and what the highest possible number is? It was hard for us to come up with a reasonably low upper bound so that I have no idea whether this solution is close to the maximum.

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  • 3
    That's what I meant by "legal".
    – Simon Fromme
    Commented Jun 6, 2016 at 23:12
  • 14
    I'm glad to see this wasn't on sexuality stack exchange. ;)
    – Wildcard
    Commented Jun 7, 2016 at 2:20
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    Well having 27 queens with only 8 pawns being able to promote is rather hard to accomplish
    – Simon Fromme
    Commented Jun 9, 2016 at 4:59
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    In this position, what was Black's last move?
    – M.M
    Commented Jun 10, 2016 at 4:02
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    @M.M Very belated, but it looks like we can retract ...Ke5-e4, Rd4-d5, possibly with an uncapture on the latter, and then even ...Kf5-e5, R-f3 if needed; from there the position seems to unwind fairly reasonably.
    – Steven Stadnicki
    Commented Dec 13, 2016 at 23:54

3 Answers 3

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[FEN "1B1Q1Q2/2R5/pQ4QN/RB2k3/1Q5Q/N4Q2/K2Q4/6Q1 w - - 0 1 "]

105 mates — Nenad Petrovic, Sahovski Vjesnika 1947 (Chess Problem Database)

In this position any check is mate. There are 3 knight mates (c4, g4, f7), 23 discovered mates (14 moves for the rook on c7, 9 for the bishop on b5), and 79 queen mates: 1 on a1, 2 on b2, 3 on c3, 4 on c5, 6 on d4, 3 on d5, 6 on d6, 3 on e1, 2 on e2, 4 on e3, 4 on e4, 2 on e6, 4 on e7, 3 on e8, 5 on f4, 3 on f5, 6 on f6, 4 on g3, 5 on g5, 2 on g7, 3 on h2, 3 on h5, and 1 on h8, for a total of 105 mates.

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    Just out of interest, is this known to be the best possible? Has it been asserted to be the best that anyone has found? Or is it "just" a position with a heck of a lot of checkmates?
    – David Richerby
    Commented Jun 6, 2016 at 18:50
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    bof mentioned in a now deleted comment that he got the position from a book which didn't include any proof that the number is a maximum. Since I didn't find any useful information on the problem online I would suspect it's an open problem.
    – Simon Fromme
    Commented Jun 6, 2016 at 19:22
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    @DavidRicherby I've seen this position cited as a record in books, none of them very recent. I'm pretty sure that 105 mates was at one time the record number of mates in a legal position. I do not know if that record has been broken or if it has been proven to be a maximum.
    – bof
    Commented Jun 6, 2016 at 19:39
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    Reminds me of puzzle I saw a while ago without quite so many pieces, but with heaps of double checks and discovered checks possible, all giving mate, where the problem was white to move and not checkmate. If I remember right, the only possible solution was a bishop move that discovered a check, and covered up another piece, giving the king one escape square. Every other legal move was checkmate.
    – Jivan Scarano
    Commented Jun 6, 2016 at 23:24
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    The a6 pawn is probably there to make sure Black's last move was legal (a7-a6).
    – Glorfindel ♦
    Commented Sep 20, 2016 at 6:39
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Anthony Stewart Mackay Dickens found another solution, also with 105 mating moves, but with only 17 units in the diagram (16 white and the black king):

[title "Anthony Stewart Mackay Dickens, The Problemist, Jan 1970. 105 mates"]
[fen "2Q1Q3/2Q4Q/Q4Q2/3k4/Q5Q1/1R6/B1NBQ3/K2R1N2 w - - 0 1"]

This may be found here on PDB.

Black's last move must have been ...Kc5-d5 following Qxc7+.

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    I can imagine a video of this game as the queens chase around this king to the tune of yakety yak or something...
    – corsiKa
    Commented Jun 6, 2016 at 20:07
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    "Yakety Sax", you must mean en.wikipedia.org/wiki/Yakety_Sax
    – Noam D. Elkies
    Commented Jun 8, 2016 at 17:11
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The following version has 99 threats none of which is a discovered check. It is possibly the best under that additional requirement.

I made it as an answer to the same question asked on Puzzling SE.

enter image description here

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  • Nice - need bK e.g. h1
    – Laska
    Commented Mar 29, 2019 at 0:12

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