RECTANGULAR BOARDS

This page contains a table of optimal domination numbers for many rectangular boards
and solutions for KxN boards.


The following pages contain optimal domination numbers,
extendable solutions, and extendable proofs for rectangular boards
with a fixed number of rows and an unlimited number of columns.

1xN
2xN
3xN
4xN
5xN
6xN
7xN
8xN


This table contains the minimum number of knights to cover rectangular boards.
(OEIS A098604)
All values are optimal and have been verified using exact methods.

      1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
   +------------------------------------------------------------
 1 |  1  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
 2 |  2  4  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
 3 |  3  4  4  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
 4 |  4  4  4  4  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
 5 |  5  4  4  4  5  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
 6 |  6  4  4  4  6  8  .  .  .  .  .  .  .  .  .  .  .  .  .  .
 7 |  7  6  6  6  7  8 10  .  .  .  .  .  .  .  .  .  .  .  .  .
 8 |  8  8  8  8  8  8 11 12  .  .  .  .  .  .  .  .  .  .  .  .
 9 |  9  8  8  8  8 10 12 13 14  .  .  .  .  .  .  .  .  .  .  .
10 | 10  8  8  8  9 12 14 14 15 16  .  .  .  .  .  .  .  .  .  .
11 | 11  8  8  8 10 12 15 16 17 19 21  .  .  .  .  .  .  .  .  .
12 | 12  8  8  8 10 12 16 16 18 20 22 24  .  .  .  .  .  .  .  .
13 | 13 10 10 10 12 14 17 18 20 22 24 26 28  .  .  .  .  .  .  .
14 | 14 12 11 12 12 16 19 20 22 23 26 28 30 32  .  .  .  .  .  .
15 | 15 12 12 12 13 16 20 21 23 24 28 30 32 34 36  .  .  .  .  .
16 | 16 12 12 12 14 16 21 22 24 26 30 32 34 36 38 40  .  .  .  .
17 | 17 12 12 12 14 18 22 24 26 27 31 33 36 38 41 44 46  .  .  .
18 | 18 12 12 12 15 20 24 24 27 29 33 36 38 40 43  .  . 52  .  .
19 | 19 14 14 14 16 20 25 26 29 31 35 37 40 43  .  .  .  . 57  .
20 | 20 16 15 16 17 20 26 28 30 32 36 40 42  .  .  .  .  .  . 62
21 | 21 16 16 16 18 22 27 29 31 34 38 41
22 | 22 16 16 16 18 24 28 30 32 35 40
23 | 23 16 16 16 19 24 30 32 34 36
24 | 24 16 16 16 20 24 31 32 35 38
25 | 25 18 18 18 21 26 32 34 37 40
26 | 26 20 19 20 22 28 33 36 38 41
27 | 27 20 20 20 22 28 34 37 40