  Number the cells of a (possibly infinite) chessboard in some way with the
numbers 0, 1, 2, ... Consider the cells in order, placing a queen in a cell if
and only if it would not attack any earlier queen. The problem is to determine
the positions of the queens. We study the problem for a doubly-infinite
chessboard of size Z x Z numbered along a square spiral, and an infinite
single-quadrant chessboard (of size N x N) numbered along antidiagonals. We
give a fairly complete solution in the first case, based on the Tribonacci
word. There are connections with combinatorial games.
