KNIGHT COVERING ON LARGE BOARDS

This page contains the best-known solutions for knight coverings on large board sizes.

These solutions have been produced using approximation methods and may not be optimal.
(Other pages of this site contain solutions for smaller boards,
produced using exact methods which guarantee optimality.)

SizeKnights
30x30135
35x35181
45x45290
50x50350


The following papers contain theoretical results concerning efficient knight cover patterns.
They were used to obtain solutions for many of the large board sizes.

Efficient Center Patterns
Efficient Edge Patterns
Efficient Corner Patterns


This graph shows the average number of squares covered per knight
for the best known solutions of board sizes 8x8 through 40x40. 

     8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
5.3  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
5.4  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
5.5  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
5.6  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
5.7  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
5.8  -  X  -  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
5.9  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
6.0  -  -  -  -  X  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
6.1  -  -  -  -  -  -  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
6.2  -  -  -  -  -  -  -  -  -  -  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
6.3  -  -  X  -  -  -  -  X  -  X  -  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
6.4  -  -  -  -  -  -  -  -  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
6.5  -  -  -  -  -  -  -  -  -  -  -  -  X  X  X  X  X  X  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
6.6  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  X  X  X  -  -  -  -  -  -  -  -  -  -  -  -
6.7  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  X  X  -  -  -  -  -  -  -  -  -  -
6.8  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  X  -  -  -  -  -
6.9  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
7.0  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  X