1

For each square on the board, how many moves could a queen on that space move, including not moving?

Ideally I'd like to see this visualized but I understand if that's not possible.

  • hint: how many moves can it move within a rank? Within a file? Diagonally? Add those up. – John Dvorak Mar 24 '17 at 17:56
  • @JanDvorak I'm not familiar with that terminology, I'm a bit of a beginner – mcchucklezz Mar 24 '17 at 17:57
  • Of course this question can only be answered for an empty board, which is not what you usually have. – user1583209 Mar 24 '17 at 20:30
4

It depends on the square, but simple counting (along the rows, columns and diagonals) reveals that this is the answer:

22 22 22 22 22 22 22 22
22 24 24 24 24 24 24 22
22 24 26 26 26 26 24 22
22 24 26 28 28 26 24 22
22 24 26 28 28 26 24 22
22 24 26 26 26 26 24 22
22 24 24 24 24 24 24 22
22 22 22 22 22 22 22 22

You see that in the center, the queen controls the most squares. I'm more familiar with a similar diagram counting the number of squares a queen controls (excluding the square itself):

21 21 21 21 21 21 21 21
21 23 23 23 23 23 23 21
21 23 25 25 25 25 23 21
21 23 25 27 27 25 23 21
21 23 25 27 27 25 23 21
21 23 25 25 25 25 23 21
21 23 23 23 23 23 23 21
21 21 21 21 21 21 21 21

This is a superposition of the diagram for a bishop:

 7  7  7  7  7  7  7  7
 7  9  9  9  9  9  9  7
 7  9 11 11 11 11  9  7
 7  9 11 13 13 11  9  7
 7  9 11 13 13 11  9  7
 7  9 11 11 11 11  9  7
 7  9  9  9  9  9  9  7
 7  7  7  7  7  7  7  7

and the one for a rook, which is very simple, and a good illustration why rooks aren't at home in the center like most other pieces:

14 14 14 14 14 14 14 14
14 14 14 14 14 14 14 14
14 14 14 14 14 14 14 14
14 14 14 14 14 14 14 14
14 14 14 14 14 14 14 14
14 14 14 14 14 14 14 14
14 14 14 14 14 14 14 14
14 14 14 14 14 14 14 14
1

It would depend on which square the Queen is. If the Queen was in on of the corner squares, it could move to the least squares possible. If the Queen was in one of the center squares, it could move to the most squares possible.

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