The non-interacting n queen's placing modeling for the n x n chess board

The non-interacting N Queen's placement on the N × N chess board attracts large attention of chess players, mathematicians, programmers, artificial intelligence systems creators. Multiple decisions are known both for a standard 8 × 8 squares chess board and for up to 1000 × 1000 squares chess boards. This paper is about computerized modeling of the N × N squares chess board for visual analysis and search for regular decisions permitting generalization for any large N. The regular decisions have been found for N = 6k + m, where k = 1, 2, 3... is any positive integer, and m = -2, -1, 0, 1. The regularization for m = 2 or 3 has appeared to be impossible. But for N = 8 and 9 the pseudoregular decisions have been found, which do not exist for k > 1. This approach demonstrates how effective may be the human-computer interaction, in which the researcher generates algorithms to solve the problem and the computer returns visual images permitting generalization and mathematical induction.