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On this chess optimization puzzle, there are only black knights and white queens. Your aim is that no black knight is threatened and to maximize the total number of queens the knights could capture. You can use as many knights and queens as you want.

On the following very low example, the score for black knights is 8.

enter image description here

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    $\begingroup$ Can we use more than 4 black knights? $\endgroup$
    – Dmitry Kamenetsky
    May 15, 2020 at 3:08
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    $\begingroup$ @DmitryKamenetsky yes! You can use as many knights as you want from 1 to 63! Same for white queens $\endgroup$
    – JKHA
    May 15, 2020 at 3:14

2 Answers 2

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7
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I've been trying to beat the benchmark for a couple of days, and I have not been able to. However, I can tie it.

Also 24
Chessboard
(lichess)

Although it was unintentional, all queens here are also in the first answer, and all knights in the first answer are here. I'm going to have to be happy having tied while using an equal number of knights and queens (and 4 fewer pieces).

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8
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Just to set a basemark, by extending your example, I can get to

24
enter image description here
(link)

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    $\begingroup$ Wanting to set a basemark you equaled my best score, I'm very curious to know if someone's gonna beat it or if someone could prove this is the optimal value $\endgroup$
    – JKHA
    May 14, 2020 at 10:15
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    $\begingroup$ I've seen a couple users here who are very skilled in integer programming, I'm sure they can find the optimal solution. $\endgroup$
    – Glorfindel
    May 14, 2020 at 10:20
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    $\begingroup$ Oh! people solve such problems with integer programming! I didn't think of this idea, but now it's obvious that's a great idea for solving them... I'm even gladder I post my puzzle haha $\endgroup$
    – JKHA
    May 14, 2020 at 10:40

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