What is the highest number of different mates in 1 you can have in one (legal) position?

Question

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.

Note that this question didn't impose the requirement for a position to be legal. — Simon Fromme, Jun 06 '16 at 05:48
It also apparently doesn't impose the requirement that the position be reachable in a real game. Or is that what you meant? — Michael, Jun 06 '16 at 23:10
@Glorfindel I assume 141 (from the Puzzling.SE Q) is a legal answer, then? Is it strange that nobody has posted it here yet? — PythonNut, Jun 09 '16 at 04:56
Well having 27 queens with only 8 pawns being able to promote is rather hard to accomplish — Simon Fromme, Jun 09 '16 at 04:59
@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, Dec 13 '16 at 23:54

score 28 · Answer 1 · edited Aug 20 '19 at 20:18

28

[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.

edited Aug 20 '19 at 20:18

Rewan Demontay

17,514
4
67
113

answered Jun 06 '16 at 06:22

bof

3,782
1
19
33

Thank you! Did you just get this from a book or do you also know if that's proven to be the maximum or have any additional information? – Simon Fromme Jun 06 '16 at 07:09
What's wrong with putting the knight from a3 to b2, allowing not one but two mates with it (Kc4# or Kd3#)? – YSC Jun 06 '16 at 11:44
@YSC You gain one knight mate but lose two queen mates, Qbb2# and Qdb2#. – bof Jun 06 '16 at 12:00
@bof You're right! – YSC Jun 06 '16 at 13:10
You would even lose three queen mates (Qa1# too) – Simon Fromme Jun 06 '16 at 13:27
2

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 Jun 06 '16 at 18:50
1

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 Jun 06 '16 at 19:22
2

@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 Jun 06 '16 at 19:39
White to move and draw. 😉 – Jivan Scarano Jun 06 '16 at 23:02
1

@JivanScarano Too many solutions: 1.Qxa6 or 1.Rxa6 or 1.Ka1 axb5 2. Ba7 etc. etc. – bof Jun 06 '16 at 23:13
2

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 Jun 06 '16 at 23:24
1

@JivanScarano Is this it? – bof Jun 07 '16 at 00:04
1

Yep, that's the one. 1.Rc6(+) allows Rxh7, because the rook is no longer pinned by the Ba8. – Jivan Scarano Jun 07 '16 at 00:10
5

The a6 pawn is probably there to make sure Black's last move was legal (a7-a6). – Glorfindel Sep 20 '16 at 06:39
@JivanScarano It has come up again here. – boboquack Nov 17 '17 at 09:16

score 20 · Answer 2 · answered Jun 06 '16 at 08:52

20

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+.

answered Jun 06 '16 at 08:52

Rosie F

6,305
2
19
36

6

I can imagine a video of this game as the queens chase around this king to the tune of yakety yak or something... – corsiKa Jun 06 '16 at 20:07
2

"Yakety Sax", you must mean https://en.wikipedia.org/wiki/Yakety_Sax – Noam D. Elkies Jun 08 '16 at 17:11

Arnaud Mortier · Answer 3 · 2019-04-25T11:46:08.963

8

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.

edited Apr 25 '19 at 11:46

answered Mar 28 '19 at 23:08

Arnaud Mortier

223
3
6

Nice - need bK e.g. h1 – Laska Mar 29 '19 at 00:12

What is the highest number of different mates in 1 you can have in one (legal) position?

3 Answers3