Another 'easy to state, hard to solve' maths/chess problem has been solved recently. The N-Queen problem now has an approximate answer to the question "How many arrangements can you have of n queens on and n by n chessboard, so that no queen attacks another?" For a standard board (8x8) it has been long known that there are 92 distinct arrangements, but this problem is the general nxn case, where n can be an extremely large number.
The solution (0.143n)^n is of course an approximation (rather than an exact number), but it is close enough to the correct number for all n. If you want to see how this number was arrived at then a link to the paper is here. There is also a good article explaining what works was done to arrive at this number, while if you want to test some of the smaller solutions, there there is some python code here.
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