I would like to share some interesting results of playing with the N-Queens Problem solver. The following plots represent distribution of the solutions number depending on the arrangement of a subset of queens. This distribution is built by iterating the possible permutations of such a subset and counting the number of all solutions containing the current permutation (i.e. by solving N-Queens Completion Problem for each permutation).
In this particular case, subset consists of three queens that occupy the first three adjacent columns and only the permutations without overlaps (no one attacks each other) are enumerated. The subset length affects the resolution of the plot but not the general nature of the distribution.
Here you can see results and data for N = 13, 14 ... 17