How can 3 queens control the white squares?

Question

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?

Answer 1

I think this will do it

Arrange three queens as follows

Answer 2

I think this arrangement works for the bonus question:

Answer 3

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.

Summary:

The expected answer is @Zoir's; with the bonus requirement it is unique up to the obvious symmetries.


Without the bonus requirement there are an additional 3 1/2 properly distinct solutions 2 of which have been given by
@hexomino


and @mpasko256

Notes:

@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:

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

Answer 4

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

Answer 5

@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:

_{Source code for the above program}