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In discrete geometry, the original orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane. It is also called the tree-planting problem or simply the orchard problem. There are also investigations into how many k-point lines there can be. Hallard T. Croft and Paul Erdős proved tk > c n / k, where n is the number of points and tk is the number of k-point lines. Their construction contains some m-point lines, where m > k. One can also ask the question if these are not allowed.
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