It is well known that there is no way of arranging 4 queens on a checker board in such a way that every square is occupied or threatened.

Now consider a slight variation where we only need to cover one color:

Can you place 3 queens on a standard 8x8 checker board such that every white square is occupied or threatened?

Bonus: What if the queens are not allowed to attack each other?

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    $\begingroup$ Please do not use intentionally provocative framings. The original phrasing of this question referenced backlash against racial justice movements — backlash that has led directly to the deaths of several activists, and has put people's lives at risk (including some people who visit PSE!). Phrasing the question in that way does not improve the puzzle content in any way, and it trivializes the lives of the many people who have been killed in racially-motivated crimes. $\endgroup$
    – Deusovi
    Feb 6, 2021 at 4:20
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    – bobble
    Feb 7, 2021 at 0:04
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    $\begingroup$ Edits to this question are being discussed on meta. $\endgroup$ Feb 7, 2021 at 5:25
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    $\begingroup$ Confused - is this about checkers where only one colour o fthe board is played with anyway, but the powerful stones are calle dkings? Or is it about chess, where the board is commonly referred to as chess board? $\endgroup$ Feb 7, 2021 at 15:23
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    $\begingroup$ @HagenvonEitzen i don't think it matters. however, if you really have to choose one, i'd say: seeing that no checkers pieces are here, but queen pieces are, and part of the puzzle focuses on the movement of the queens in chess, i'd say it's chess $\endgroup$
    – oAlt
    Feb 7, 2021 at 15:32

5 Answers 5


I think this will do it

Arrange three queens as follows
enter image description here

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    $\begingroup$ Whoa, that was quick. Well done. I shall add a bonus question. $\endgroup$ Feb 4, 2021 at 19:02

I think this arrangement works for the bonus question:

enter image description here

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    $\begingroup$ Yep, that's the one I had in mind. Well done! $\endgroup$ Feb 4, 2021 at 20:34
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    $\begingroup$ @hexomino was first, so I had to accept his answer, but I'll place a small bounty on this one, once it is possible. $\endgroup$ Feb 4, 2021 at 20:47

Just a summary of the answers by @hexomino, @Zoir and @mpasko256, a few notes and perhaps (if nobody else finds it within the next few days) one more solution.


The expected answer is @Zoir's; with the bonus requirement it is unique up to the obvious symmetries.
![enter image description here

Without the bonus requirement there are an additional 3 1/2 properly distinct solutions 2 of which have been given by
enter image description here

and @mpasko256
enter image description here


@hexomino's solution is the only one that also works on a 9x9 board (with white corners).
@mpasko256's can be shifted 1 square diagonally. That is what I counted as half a solution above.

More solutions:

The shifted solution:
enter image description here

And there is one more solution which I'll add in a few days.


As I see, bonus question is already solved. But it must mean that non-bonus can have multiple solutions. I present my own:

My solution to 3 queens problem without bonus


@PaulPanzer made a summary of existing answers here (including some they gave themselves).

I want to provide a clearer visualization for each of the existing solutions:

enter image description here

Source code for the above program


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