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How many horses do you need to attack the whole board? To control the whole board?

Answer: Fourteen horses to attack all board cells:

  1 2 3 4 5 6 7 8
  ___ ___ ___ ___ ___ ___ ___ ___
 H |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 G |  | | |  | | |  N |  N |  N |  N |  | | |  | | |
  --- --- --- --- --- --- --- ---
 F |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 E |  | | |  N |  N |  | | |  | | |  N |  N |  | | |
  --- --- --- --- --- --- --- ---
 D |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 C |  | | |  N |  N |  N |  N |  N |  N |  | | |
  --- --- --- --- --- --- --- ---
 B |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 A |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- --- 
You can use this option:
  1 2 3 4 5 6 7 8
  ___ ___ ___ ___ ___ ___ ___ ___
 H |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 G |  | | |  | | |  N |  | | |  | | |  N |  | | |  | | |
  --- --- --- --- --- --- --- ---
 F | |  | | |  | | |  N |  N |  N |  N |  | | |  | | |
  --- --- --- --- --- --- --- ---
 E |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 D |  | | |  | | |  N |  N |  N |  N |  | | |  | | |
  --- --- --- --- --- --- --- ---
 C |  | | |  N |  N |  | | |  | | |  N |  N |  | | |
  --- --- --- --- --- --- --- ---
 B |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 A |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- --- 
To control (attack, or occupy) all the cells of the board, 12 horses are enough:
  1 2 3 4 5 6 7 8
  ___ ___ ___ ___ ___ ___ ___ ___
 A |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 B |  | | |  | | |  N |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 C |  | | |  | | |  N |  N |  | | |  N |  N |  | | |
  --- --- --- --- --- --- --- ---
 D |  | | |  | | |  | | |  | | |  | | |  N |  | | |  | | |
  --- --- --- --- --- --- --- ---
 E |  | | |  | | |  N |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---
 F |  | | |  N |  N |  | | |  N |  N |  | | |  | | |
  --- --- --- --- --- --- --- ---
 G |  | | |  | | |  | | |  | | |  | | |  N |  | | |  | | |
  --- --- --- --- --- --- --- ---
 H |  | | |  | | |  | | |  | | |  | | |  | | |  | | |  | | |
  --- --- --- --- --- --- --- ---