How many queens does it take to attack or control the board?

competition/games/chess/queen.control

Problem

How many queens does it take to attack or control the board?

Show solution

Five queens are required to attack every square:

    1   2   3   4   5   6   7   8
   ___ ___ ___ ___ ___ ___ ___ ___
h |   |   |   |   |   |   |   |   |  
   --- --- --- --- --- --- --- ---
g |   |   |   | Q |   |   |   |   |
   --- --- --- --- --- --- --- ---
f |   |   |   | Q |   |   |   |   |
   --- --- --- --- --- --- --- ---
e |   |   |   | Q |   |   |   |   |
   --- --- --- --- --- --- --- ---
d |   |   |   | Q |   |   |   |   |
   --- --- --- --- --- --- --- ---
c |   |   |   |   |   |   |   |   |
   --- --- --- --- --- --- --- ---
b |   |   |   |   |   |   |   |   |
   --- --- --- --- --- --- --- ---
a |   |   |   | Q |   |   |   |   |
   --- --- --- --- --- --- --- ---

There are other positions with five queens.