No-Three-in-Line Problem

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In 1917, Henry Dudeney asked for the maximum number of points selectable from an × grid so that no three points are collinear. Obviously, no more than two points can be selected from any row or column, so the maximal amount of points is . Calling a solution an × grid with a maximal selection of points with no three points collinear, a 52×52 grid with 104 selected points is the largest known solution. This Demonstration gives all solutions up to order 18×18, and some of the known solutions for larger-sized grids.

Contributed by: Ed Pegg Jr (November 2013)
Open content licensed under CC BY-NC-SA



Solution data for orders 17 and 18 are from [2]. All other solution data is from [1].


[1] A. Flammenkamp. "The No-Three-in-Line Problem." (Mar 3, 1998)

[2] B. Chaffin. "No Three In Line Problem." (Apr 4, 2006) _line/index.htm.

[3] Wikipedia. "No-Three-in-Line Problem." (Nov 5, 2013)

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