Counting How Many Queens Are Placed Tentatively
While Seeking A First Solution To The N x N Queens Puzzle.

For this example we'll use a 5 x 5 board because this size requires the fewest number of
tentative Queen placements (only 15) to reach the first solution to the puzzle.

A Queen shown in RED is obviously clashing with at least one previously-placed Queen.
It will be lifted off the board and set down again (or be "placed") in the next unoccupied square.
When a Queen is placed with no clashes on any row, we immediately move up to the next row.

We have FOUND the first possible solution to the 5 x 5 version of the N-Queens puzzle!
This example also shows that when placing Queens in this manner, no 'earlier' solutions can exist.

	15	The 15th 'placement' of a Queen results in this first solution to our puzzle.
	5	Number of times a Queen was placed on the board, and was allowed to stay.
	10	Number of times a Queen was placed on the board, but was clearly challenged by at least one previously-placed Queen.

Queen-placement example page  15  of   15


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CSP Queens - Analysis Of The N-Queens Puzzle © 1975 by Colin S Pearson and Martin S Pearson is licensed under CC BY-NC-SA 4.0 Permissions beyond the scope of this license may be available via the feedback page.

Page updated:  14 July 2025