How many queens can be on the board without neither forced mate nor forced stalemate (53?)?

Question

I was wondering how many queens can be put on boards without the position being a forced checkmate or a forced stalemate. The best I came up with is 53 this position.

[FEN "QQQQQRK1/QQQQQPr1/QQQQQRNk/QQQQQQpB/QQQQQQQQ/QQQQQQQQ/QQQQQQQQ/QQQQQQQQ w - - 0 1"]

Is there a way to fit 54 or more queens, given the constraints)? And if not, how would one show that more queens cannot be placed?

Andrew Chin · Accepted Answer · 2020-06-06T19:15:40.220

10

57 Queens:

[FEN "QQQQQB1k/QQQQQ1bq/QQQQQQKB/QQQQQQQQ/QQQQQQQQ/QQQQQQQQ/QQQQQQQQ/QQQQQQQQ b - - 0 1"]

(edited FEN, White to move).
(2edited, thanks Noam D. Elkies)

edited Jun 06 '20 at 19:15

answered Jun 05 '20 at 10:14

Andrew Chin

863
7
7

1

It is not clear in the OP, but I imagine the side with the queens was supposed to be on the move ? – Evargalo Jun 05 '20 at 10:46
2

@Evargalo Then imagine White King on b3 to start. Kc2 is the only legal move. – Andrew Chin Jun 05 '20 at 10:48
Sure, this solution is valid then. – Evargalo Jun 05 '20 at 10:49
If white has the move then change a3 to a queen – IKnowNothing Jun 05 '20 at 12:02
If you swap the Ba3 with a knight, you can put another queen in b3 and white still has a legal move. – Federico Poloni Jun 05 '20 at 18:15
@FedericoPoloni yes, and White has a forced win, which is what we need to avoid. – Andrew Chin Jun 05 '20 at 18:17
@AndrewChin Does it? What if white just moves the knight back and forth while black takes all the pieces? Or maybe I don't understand what you mean with "forced win". – Federico Poloni Jun 05 '20 at 18:40
2

I think you can squeeze one more Queen out of this nice setup by changing the Ba2 to a Black Queen for a total of 57. – Noam D. Elkies Jun 06 '20 at 17:29
3

Whoa, you're right! The question didn't say Queens of only one colour! – Andrew Chin Jun 06 '20 at 19:14

How many queens can be on the board without neither forced mate nor forced stalemate (53?)?

1 Answers1