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You've most likely heard of the eight queens puzzle, right? Where you have to place n chess queens on an n * n board so that no queens attack each other (boy, those must be some very angry monarchs!)? Well...what if, instead of queens, you had to place chess knights on an n * n board?

What's the maximum possible number of chess knights you can place on a 4 by 4 grid so that no knight can attack at least one knight in one single move? What about a 5 by 5 grid? A 6 by 6? A 7 by 7? Is there even a pattern to the maximum number of knights you can place on an n by n grid so that nobody attacks another knight? (You don't need to answer that last question, but don't let that stop you from answering it if you really want to! It's just an extension question!)

Edit: And here's another question!

For an n by n board how many ways are there of placing knights according to the rules given?

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  • $\begingroup$ If you re-post this in the Sandbox, it can be adjusted to not be a duplicate, if you're interested. $\endgroup$
    – Hazel へいぜる
    Sep 21, 2021 at 19:16
  • $\begingroup$ We have a close reason called "Needs More Focus" for when there are too many questions in a question. Adding a new question will not make this a non-duplicate; removing the duplicate questions and keeping the new question would. $\endgroup$
    – bobble
    Sep 22, 2021 at 16:21

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For a 4 by 4 grid:

4 by 4 grid chessboard, knights on all black squares or all white squares

5 by 5 grid:

5 by 5 grid, kinghts on white squares. They can also be on black squares

6 by 6:

6 by 6 grid, knights on white squares or black.

7 by 7:

7 by 7 grid, knights on white or black squares

Why?

When a knight moves, it moves to a space of a different color (from white to black or black to white). If they are all on the same color, no collision happens.

Pattern: The pictures speak for themselves.

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    $\begingroup$ You can improve your 7x7 solution by one, by replacing the 24 white-square knights with 25 black-square knights. $\endgroup$
    – Penguino
    Sep 22, 2021 at 4:33

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