The N Queens Puzzle

We used a very simple algorithm to identify the first possible solution to the puzzle on any size of chessboard. It's essentially trial-and-error, placing a Queen and then seeing if it fits. However, I developed my own variation on Dad's original algorithm, eliminating "at risk" squares in advance instead of checking for threats every time a new Queen was placed, and it is this variation that I used when Seeking The First Solution.

Having found all these solutions, we then needed a way of keeping track of them so we came up with this even simpler notation for Describing Solutions. I've used this notation in the List of First Solutions, and each solution also has a link to a chessboard diagram. Also given is the number of Queens placed on each size of chessboard whilst seeking that first solution, an interesting by-product of our algorithm.

In April 2011, another mathematician with whom we'd been corresponding since October 2010 offered us a first solution for the 46 by 46 chessboard, upon which our program had been working for a number of years. By July 2011 - using a copy of his program - we had verified that this was indeed the first solution, and I wondered just how far away our own program was from achieving the same result. Take a look at My Estimate For 46 by 46 to see my surprising conclusions.

Amongst Dad's Counting N-Queen Puzzle Queen-placements pages he offers a free, downloadable "demo" program that you can use to generate some of our results yourself. It employs the same algorithm as the program he currently uses to find new solutions, but it's limited to chessboard sizes only up to 32 by 32.