benni<p>Inspired by the No-three-in-line-Problem <a href="https://en.wikipedia.org/wiki/No-three-in-line_problem" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/No-three</span><span class="invisible">-in-line_problem</span></a> i studied a much simpler case and came up with a mini-conjecture:</p><p>Definition: A position on a Grid is called "blocked" if there would be three in Line, if a point is placed there.</p><p>Conjecture: You can't place n points on a n x n Grid without blocking a point or putting 3 in a line for n > 4.</p><p>Any hints on proving or disproving it? I am pretty sure it is true.</p><p><a href="https://social.tchncs.de/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://social.tchncs.de/tags/NoThreeInLineProblem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>NoThreeInLineProblem</span></a> <a href="https://social.tchncs.de/tags/DiscreteGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DiscreteGeometry</span></a></p><p>(edited after comments)</p>