GENERALIZATIONS OF THE NO-THREE-IN-A-LINE PROBLEM

摘要

The no-three-in-line problem has been around for nearly a hundred years: How many points can be selected on an empty n × n grid, without having more than two on the same line? The generalization we propose has been considered in a different context by Gossell and Johnson [4]: How many points can be placed on the grid without them forming an "ell," or a right angle? We provide a different proof from that in [4],and state some open problems that might be considered by readers of Geombinatorics.