Inspired by the No-three-in-line-Problem https://en.wikipedia.org/wiki/No-three-in-line_problem i studied a much simpler case and came up with a mini-conjecture:
Definition: A position on a Grid is called "blocked" if there would be three in Line, if a point is placed there.
Conjecture: You can't place n points on a n x n Grid without blocking a point.
Any hints on proving or disproving it? I am pretty sure it is true, but did not spend much time trying to prove it.
#math #NoThreeInLineProblem #DiscreteGeometry
benni
npub195…r2d07
2024-09-07 09:35:02 UTC
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2024-09-07 09:35:02 UTCEvent JSON
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"content": "Inspired by the No-three-in-line-Problem https://en.wikipedia.org/wiki/No-three-in-line_problem i studied a much simpler case and came up with a mini-conjecture:\n\nDefinition: A position on a Grid is called \"blocked\" if there would be three in Line, if a point is placed there.\n\nConjecture: You can't place n points on a n x n Grid without blocking a point.\n\nAny hints on proving or disproving it? I am pretty sure it is true, but did not spend much time trying to prove it.\n\n#math #NoThreeInLineProblem #DiscreteGeometry",
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