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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 &gt; 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>
Mircea<p><a href="https://masto.ai/tags/Introdiction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Introdiction</span></a> : I'm a mathematician moving towards data science topics, based in Chile. Some interests:<br><a href="https://masto.ai/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>geometry</span></a> <a href="https://masto.ai/tags/datageometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>datageometry</span></a> <a href="https://masto.ai/tags/discretegeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>discretegeometry</span></a> <a href="https://masto.ai/tags/materialscience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>materialscience</span></a> <br><a href="https://masto.ai/tags/hyperbolicneuralnetwork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>hyperbolicneuralnetwork</span></a><br><a href="https://masto.ai/tags/GraphNeuralNetwork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GraphNeuralNetwork</span></a> <a href="https://masto.ai/tags/GNNs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GNNs</span></a><br><a href="https://masto.ai/tags/topology" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>topology</span></a> <a href="https://masto.ai/tags/TDA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>TDA</span></a> <a href="https://masto.ai/tags/metricspaces" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>metricspaces</span></a><br><a href="https://masto.ai/tags/equivariantneuralnetwork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>equivariantneuralnetwork</span></a> <a href="https://masto.ai/tags/enns" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>enns</span></a> <a href="https://masto.ai/tags/convolutionalneuralnetwork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>convolutionalneuralnetwork</span></a> <a href="https://masto.ai/tags/networkscience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>networkscience</span></a> <br><a href="https://masto.ai/tags/computationalchemistry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>computationalchemistry</span></a> <a href="https://masto.ai/tags/dft" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>dft</span></a> <a href="https://masto.ai/tags/pinns" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>pinns</span></a><br><a href="https://masto.ai/tags/optimaltransport" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>optimaltransport</span></a> <br><a href="https://masto.ai/tags/learningTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>learningTheory</span></a> <a href="https://masto.ai/tags/generalization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>generalization</span></a> <br><a href="https://masto.ai/tags/expressivity" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>expressivity</span></a> <br><a href="https://masto.ai/tags/marinescience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>marinescience</span></a> <a href="https://masto.ai/tags/biodiversity" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>biodiversity</span></a> <a href="https://masto.ai/tags/oceanscience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>oceanscience</span></a> <br><a href="https://masto.ai/tags/phylogenetics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>phylogenetics</span></a></p>