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

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?

57 Queens:

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

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

• It is not clear in the OP, but I imagine the side with the queens was supposed to be on the move ? Commented Jun 5, 2020 at 10:46
• @Evargalo Then imagine White King on b3 to start. Kc2 is the only legal move. Commented Jun 5, 2020 at 10:48
• Sure, this solution is valid then. Commented Jun 5, 2020 at 10:49
• 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. Commented Jun 6, 2020 at 17:29
• Whoa, you're right! The question didn't say Queens of only one colour! Commented Jun 6, 2020 at 19:14