-3
$\begingroup$

Given the size of board (n) and the position of the queen (r,c) how can we calculate the total number of squares which can be controlled by the queen?

$\endgroup$

closed as off-topic by elias, Glorfindel, user58, Beastly Gerbil, Rubio Jan 29 '17 at 22:23

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – elias, Glorfindel, Beastly Gerbil, Rubio
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 4
    $\begingroup$ You can count them! :D $\endgroup$ – boboquack Jan 29 '17 at 8:29
5
$\begingroup$

Assuming the queen controls its own square and 0-based indexing, we have:

  • $1$ - its own square
  • $2n-2$ - the rows and columns without its own square
  • $n-1-|r+c-n+1|$ - the number of squares on one diagonal
  • $n-1-|r-c|$ - the number of squares on the other diagonal

Add them all up and we have:

$$4n-3+|r+c-n+1|+|r-c|$$

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.