Unsolved Math: The No-Three-In-Line Problem #SOME3

Comments · 328

• MA

  @mayviepixelcanon · 3 years ago

  i was literally just thinking about this, i mess around a ton in scrap mechanic and hate when i can't see what gates in a line are connected or not, and this is literally the problem that would solve that issue

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• TH

  @TheArtikae · 3 years ago

  As far as lower bounds go, you can always place at least two points. That’s my contribution. Hope it helps.

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• QU

  @QuantumHistorian · 3 years ago

  Very nice, but the over usage of stock photos and footage is distracted IMO. You can trust your explanations and the maths itself to keep the user engaged.

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• FI

  @fiartruck0125 · 3 years ago

  In 2002 or 2003 I did a summer REU (research experience for undergraduates) on a variant of this problem with triangle grids instead of squares.  A few weeks in I had a nice culled-branch search program coded up in C, but other than that I wasn't making any progress so we switched to a different topic.

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• PA

  @pafnutiytheartist · 3 years ago

  If I understand correctly, based on this video and Wikipedia, no N is known for which we definitely can&apos;t place 2N points. And for n ≤ 46 there are 2N solutions. <br>I feel like the answer might be just a clean 2N but it&apos;s too tricky to prove.

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• YA

  @yash1152 · 3 years ago

  <a href="https://www.youtube.com/watch?v=eFlATdsDaj4&amp;t=427">7:07</a> this is probably the nicest or say most tangible example in my memory so far why knowing of primes is useful. <br><br>it gives u anchor points about divisibility &amp; divisibility comes up a lot in maths.

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• ΠΑ

  @ΠαναγιώτηςΓιόφτσος · 3 years ago

  That&apos;s a great video! Pretty easy to follow, interesting and simple problem, not super handwavy, but also not extremely advanced. I&apos;m sure you&apos;ll be featured in grants video. Great work!

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• GA

  @Ganerrr · 3 years ago (edited)

  inb4 the next step to this puzzle is some equivalence to an incomprehensible conjecture about modular forms

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• JE

  @jerry3790 · 3 years ago

  I may be a lowly engineering student, but it would be cool to solve one of these smaller problems one day

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• JA

  @jaspermcjasper3672 · 5 days ago

  Thank you for using the notation &quot;y = (x squared) mod p&quot; instead of &quot;y&quot; followed by a three-bar equals sign (for &quot;is congruent to&quot;) followed by &quot;x squared&quot;, all of that in parentheses, followed by a note &quot;mod p&quot; , which is needlessly complicated.

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• BI

  @Bill_W_Cipher · 1 year ago

  Its difficult to even brute force a particular solution to this problem. For a 100 by 100 grid, there is already about 9x10^58 different arrangements you have to check.

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• JX

  @jxtq27 · 3 years ago

  at <a href="https://www.youtube.com/watch?v=eFlATdsDaj4&amp;t=44">0:44</a> the point with the checkmark is in line with points 6 and 8

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