The N Queens Puzzle

List of First Solutions

This page lists the first possible solutions to the n Queens on an n by n chessboard puzzle for various sizes of chessboard, as well as the numbers of Queens it is necessary to place whilst seeking those first solutions using our algorithm. With two notable exceptions, the final Queen to be placed completes the first solution. The two exceptions are chessboard sizes 2 by 2 and 3 by 3, for which no solutions exist. Their "Number of Queens placed" values below are therefore the total numbers of Queen placements needed to search the entire chessboard.

All of the solutions and Queen placement counts have been generated by a simple program written by my Dad, Colin using C++Builder. This is in fact the latest in a long line of similar programs that he's written to work on this puzzle over the years, beginning way back in 1975 using Assembly Language on a big, slow old mainframe computer! The results for all chessboard sizes up to 39 by 39 have been verified by a program I wrote independently in July 2008 using Turbo Pascal 7.01 (DOS Version), and I hope to verify the results for the higher chessboard sizes in due course. Further results will be added to this page as they are generated.

We have found surprisingly few consistent patterns in the numbers of Queens placed whilst seeking the first solutions. As one might expect, there is a general trend for the numbers to increase along with the chessboard sizes, but within this trend the numbers actually fluctuate up and down quite considerably. The only consistent patterns we've identified so far are as follows:

The numbers of Queens placed whilst seeking the first solutions were accepted into The On-Line Encyclopedia of Integer Sequences (OEIS) on 26th June 2008 as sequence A140450. In addition, the first solutions themselves were accepted into the OEIS on 10th July 2008 as sequence A141843.

So without further ado, here are the results of all our hard work, given in our simple co-ordinate notation. Click on the "first solution" links to see chessboard diagrams for each size of chessboard (except for 2 by 2 and 3 by 3, of course).

Chessboard Size 1 by 1

Chessboard Size 2 by 2

Chessboard Size 3 by 3

Chessboard Size 4 by 4

Chessboard Size 5 by 5

Chessboard Size 6 by 6

Chessboard Size 7 by 7

Chessboard Size 8 by 8

Chessboard Size 9 by 9

Chessboard Size 10 by 10

Chessboard Size 11 by 11

Chessboard Size 12 by 12

Chessboard Size 13 by 13

Chessboard Size 14 by 14

Chessboard Size 15 by 15

Chessboard Size 16 by 16

Chessboard Size 17 by 17

Chessboard Size 18 by 18

Chessboard Size 19 by 19

Chessboard Size 20 by 20

Chessboard Size 21 by 21

Chessboard Size 22 by 22

Chessboard Size 23 by 23

Chessboard Size 24 by 24

Chessboard Size 25 by 25

Chessboard Size 26 by 26

Chessboard Size 27 by 27

Chessboard Size 28 by 28

Chessboard Size 29 by 29

Chessboard Size 30 by 30

Chessboard Size 31 by 31

Chessboard Size 32 by 32

Chessboard Size 33 by 33

Chessboard Size 34 by 34

Chessboard Size 35 by 35

Chessboard Size 36 by 36

Chessboard Size 37 by 37

Chessboard Size 38 by 38

Chessboard Size 39 by 39

Unless otherwise stated, the results for all sizes of chessboard below this point have not yet been independently verified.

Chessboard Size 40 by 40

Chessboard Size 41 by 41

Chessboard Size 42 by 42

Chessboard Size 43 by 43

Chessboard Size 44 by 44

Chessboard Size 45 by 45

Chessboard Size 46 by 46

Chessboard Size 47 by 47

Chessboard Size 48 by 48

Chessboard Size 49 by 49

Chessboard Size 50 by 50