CSP Queens - Analysis Of The N-Queens Puzzle
Table Of First-Solutions

This is just one of many pages from my analysis of the N-Queens puzzle, on which I've worked as a pastime since 1975.  More recently, in collaboration with my son Martin, this analysis has 'expanded' from these now mundane 2-dimensional boards, into much more challenging 3-dimensional Cube versions of the puzzle.
The table below shows the Queen-position coordinates for the 'first possible' solutions on 44 different board sizes for the "N-Queens on an N x N chessboard" puzzle. I'll add more solutions as they're solved.
I define a "first solution" to this N-Queens puzzle as follows:
  1. Assuming we start with a blank chess board, and assuming we use the simple, step-by-step search algorithm which I describe here, we will step - laboriously, mechanically, sequentially and reliably - through every possible "no not yet" arrangement of Queens.
  2. The first possible solution is the first arrangement of Queens which allows all N Queens to sit uncontested on the board.
  3. From this first possible solution onwards, as our algorithm searches sequentially for the millions of other solutions per board size, we can guarantee that every new solution we find will comprise a different and 'later' pattern of Queens.

Queen-Position Coordinates For The 'First' Solutions To The "N Queens On An N x N Chessboard" Puzzle
Size of
Board
4 x 4 2 4 1 3
5 x 5 1 3 5 2 4
6 x 6 2 4 6 1 3 5
7 x 7 1 3 5 7 2 4 6
8 x 8 1 5 8 6 3 7 2 4
9 x 9 1 3 6 8 2 4 9 7 5
10 x 10 1 3 6 8 10 5 9 2 4 7
11 x 11 1 3 5 7 9 11 2 4 6 8 10
12 x 12 1 3 5 8 10 12 6 11 2 7 9 4
13 x 13 1 3 5 2 9 12 10 13 4 6 8 11 7
14 x 14 1 3 5 7 12 10 13 4 14 9 2 6 8 11
15 x 15 1 3 5 2 10 12 14 4 13 9 6 15 7 11 8
16 x 16 1 3 5 2 13 9 14 12 15 6 16 7 4 11 8 10
17 x 17 1 3 5 2 8 11 15 7 16 14 17 4 6 9 12 10 13
18 x 18 1 3 5 2 8 15 12 16 13 17 6 18 7 4 11 9 14 10
19 x 19 1 3 5 2 4 9 13 15 17 19 7 16 18 11 6 8 10 12 14
20 x 20 1 3 5 2 4 13 15 12 18 20 17 9 16 19 8 10 7 14 6 11
21 x 21 1 3 5 2 4 9 11 15 21 18 20 17 19 7 12 10 8 6 14 16 13
22 x 22 1 3 5 2 4 10 14 17 20 13 19 22 18 8 21 12 9 6 16 7 11 15
23 x 23 1 3 5 2 4 9 11 13 18 20 22 19 21 10 8 6 23 7 16 12 15 17 14
24 x 24 1 3 5 2 4 9 11 14 18 22 19 23 20 24 10 21 6 8 12 16 13 7 17 15
25 x 25 1 3 5 2 4 9 11 13 15 19 21 24 20 25 23 6 8 10 7 14 16 18 12 17 22
26 x 26 1 3 5 2 4 9 11 13 15 21 23 25 20 22 24 26 10 7 16 12 8 6 18 14 19 17
27 x 27 1 3 5 2 4 9 11 13 15 17 19 23 25 27 24 26 6 10 7 16 8 12 14 21 18 20 22
28 x 28 1 3 5 2 4 9 11 13 15 17 23 25 22 28 26 24 27 7 12 16 18 8 10 14 20 6 21 19
29 x 29 1 3 5 2 4 9 11 13 15 6 20 24 26 21 29 27 25 28 8 12 7 16 10 17 22 14 18 23 19
30 x 30 1 3 5 2 4 9 11 13 15 7 23 26 28 25 22 24 30 27 29 16 12 10 8 6 18 20 17 14 21 19
31 x 31 1 3 5 2 4 9 11 13 15 6 18 23 26 28 31 25 27 30 7 17 29 14 10 8 20 12 16 19 22 24 21
32 x 32 1 3 5 2 4 9 11 13 15 6 18 24 26 30 25 31 28 32 27 29 16 19 10 8 17 12 21 7 14 23 20 22
33 x 33 1 3 5 2 4 9 11 13 15 6 8 25 27 33 31 23 28 26 29 32 30 16 18 12 10 17 7 14 21 19 24 22 20
34 x 34 1 3 5 2 4 9 11 13 15 6 18 20 26 28 31 33 27 29 34 32 30 12 10 7 16 19 8 22 14 25 17 24 21 23
35 x 35 1 3 5 2 4 9 11 13 15 6 8 19 24 26 31 29 32 35 33 28 30 17 7 34 10 18 16 14 12 20 25 23 21 27 22
36 x 36 1 3 5 2 4 9 11 13 15 6 8 22 27 32 30 33 24 29 35 28 34 31 14 36 17 12 16 7 10 20 25 19 26 18 23 21
37 x 37 1 3 5 2 4 9 11 13 15 6 8 19 21 23 30 34 29 35 33 31 37 32 36 16 7 10 20 14 12 18 26 17 22 28 25 27 24
38 x 38 1 3 5 2 4 9 11 13 15 6 8 19 21 29 31 33 36 30 28 38 34 32 37 35 20 18 12 14 23 7 10 25 17 22 16 26 24 27
39 x 39 1 3 5 2 4 9 11 13 15 6 8 19 7 25 30 37 33 28 32 38 35 39 31 36 34 21 17 20 14 12 10 23 16 18 22 29 26 24 27
40 x 40 1 3 5 2 4 9 11 13 15 6 8 19 21 23 30 32 34 36 38 40 31 33 35 37 39 20 22 14 18 10 12 24 17 7 28 26 16 29 27 25
41 x 41 1 3 5 2 4 9 11 13 15 6 8 19 7 22 25 30 32 37 39 33 38 40 34 36 41 35 18 23 10 12 16 20 17 14 21 28 26 31 29 27 24
42 x 42 1 3 5 2 4 9 11 13 15 6 8 19 21 23 25 32 34 36 38 40 42 33 35 37 39 41 16 7 24 20 14 17 26 10 12 30 28 18 31 22 27 29
43 x 43 1 3 5 2 4 9 11 13 15 6 8 19 7 22 24 26 37 39 34 38 35 33 42 36 41 43 40 20 14 17 10 12 28 18 16 27 25 21 32 30 23 31 29
44 x 44 1 3 5 2 4 9 11 13 15 6 8 19 7 22 24 32 35 38 41 33 42 37 34 43 39 36 44 40 21 25 18 14 12 20 16 29 10 23 27 30 17 31 26 28
45 x 45 1 3 5 2 4 9 11 13 15 6 8 19 7 22 10 29 31 36 40 42 32 38 43 39 44 35 37 45 41 21 18 24 14 12 23 16 20 17 28 25 34 26 33 30 27
46 x 46 1 3 5 2 4 9 11 13 15 6 8 19 7 22 10 29 31 38 44 32 45 ? ? ? W O R K I N P R O G R E S S
47 x 47 1 3 5 2 4 9 11 13 15 6 8 19 7 22 10 25 29 36 39 42 44 33 38 43 46 40 37 41 45 47 21 17 24 26 12 14 16 18 20 23 34 28 30 32 27 35 31
48 x 48 1 3 5 2 4 9 11 13 15 6 8 19 7 22 10 25 28 30 38 43 12 ? ? ? W O R K I N P R O G R E S S
49 x 49 1 3 5 2 4 9 11 13 15 6 8 19 7 22 10 25 27 29 37 40 45 41 44 38 48 39 49 43 46 42 47 16 12 24 20 28 17 14 30 21 18 35 31 26 23 33 36 34 32
50 x 50 1 3 5 2 4 9 11 13 15 6 8 19 7 22 10 25 27 29 32 38 40 ? ? ? W O R K I N P R O G R E S S


Click Click for more about this coordinate scheme for an explanation of how to translate these numbers into Queen positions on a board.

Click Click for a table of tentative Queen placements for a table showing the counts of tentative Queen placements for these board sizes, and for the dates of my discoveries so far of the various First Solutions.

Click Return to the opening page to return to this site's Home page.


External Links:
On his Queens On A Chessboard web site, my son Martin presents all the same data above in graphical form, with a full 'board' diagram for every First Solution that we have discovered. He also describes his work on this puzzle in admirable detail.

Page Updated -  21st August 2010
Document made with KompoZer Content on this CSP Queens site by Colin S Pearson and Martin S Pearson is licensed under a
Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales License.
Permissions beyond the scope of this license may be available via the feedback page. 		Creative Commons License