Bizarrely, the number of fundamental solutions for the problem of these items is greater for the case when there are five of them rather than when there are six of them, for which there is only one solution.
George Polya introduced the toroidal version of the problem named for these objects and showed that the problem is only solvable when the number of them is not divisible by two or three. In Donald Knuth's paper "Reducing Links," he reduces the problem named for these things to an exact cover problem by constructing a matrix with "n to the 4th" entries in it. Bizarrely, the number of fundamental solutions for the problem of these items is greater for the case when there are five of them rather than when there are six of them, for which there is only one solution. A depth-first search backtracking algorithm for the constraint satisfaction problem named for these items was given by Dijkstra. For an n- by-n grid, these objects can be placed on the grid in a non-attacking fashion if n is four or greater. For 10 points, name these pieces that must be validly arranged on a chessboard in a problem from computer science.
George Polya introduced the toroidal version of the problem named for these objects and showed that the problem is only solvable when the number of them is not divisible by two or three.
queens [prompt on "chess pieces" or equivalents]