Superqueens

[cinelli]

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A superqueen is a chess piece which can move like a knight as well as like a queen. The figure shows how four superqueens can be placed on a 5 x 5 board so that no piece attacks another. This puzzle is similarly to place ten superqueens on a 10 x 10 board.

Cinelli

[modellingman]

Spoiler...

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This solution followed an approach which placed a superqueen in the top row (row 1). It then moved down the board a row at a time placing the superqueen for that row in the left-most column not attackable by any superqueen previously placed on the board.

Why start in column 3 of row 1?

This was the result of trial and error.

Using the same left-most approach but starting in row 1, column 1 resulted in no unattackable squares being available in row 8 after rows 1 to 7 had been allocated superqueens. This starting point did allow for placement of superqueens in rows 9 and 10 yielding placement on the board of 9 queens in total.

Starting from row 1, column 2 also resulted in no unattackable spaces being left in row 8 and then again in row 10, allowing for the placement of only 8 superqueens.

I have no idea if any other solutions exist which cannot be derived by either rotating or reflecting the solution above.




An interesting variant, perhaps, is the minimum number of superqueens required so that every square on the board is either occupied by a superqueen or attackable by one but no superqueen is attackable by any other superqueen.


modellingman

[cinelli]

Well solved, modellingman. I believe your solution is unique up to reflections and rotations.

Cinelli