I mentioned during my talk that a new solution had been announced minutes earlier.
“On 25th June 2026 Marijn Heule found a new solution with record grid size n=72 in the rot4 symmetry class.”
The solution was published during my talk. Over at MathWorld, No-Three-in-a-Line Problem, the solutions for 67 and 69 are posted.
In[]:=
nicegrid[{p_,n_}]:=Graphics[{Thin,Gray,Table[Line[{{0,k},{n,k}}],{k,0,n}],Table[Line[{{k,0},{k,n}}],{k,0,n}],Black,Rectangle[#,#+1]&/@p},AspectRatio->1,ImageSize->500]​​​​p72={{32,71},{37,71},{29,70},{38,70},{43,69},{49,69},{24,68},{30,68},{27,67},{51,67},{9,66},{43,66},{51,65},{61,65},{55,64},{57,64},{23,63},{54,63},{19,62},{66,62},{6,61},{40,61},{30,60},{44,60},{23,59},{47,59},{55,58},{56,58},{7,57},{31,57},{13,56},{21,56},{7,55},{13,55},{8,54},{36,54},{42,53},{46,53},{34,52},{62,52},{4,51},{6,51},{38,50},{56,50},{2,49},{35,49},{59,48},{63,48},{12,47},{68,47},{18,46},{45,46},{25,45},{39,45},{11,44},{67,44},{2,43},{5,43},{18,42},{70,42},{60,41},{68,41},{10,40},{57,40},{26,39},{71,39},{1,38},{21,38},{0,37},{52,37},{17,36},{49,36},{22,35},{54,35},{19,34},{71,34},{50,33},{70,33},{0,32},{45,32},{14,31},{61,31},{3,30},{11,30},{1,29},{53,29},{66,28},{69,28},{4,27},{60,27},{32,26},{46,26},{26,25},{53,25},{3,24},{59,24},{8,23},{12,23},{36,22},{69,22},{15,21},{33,21},{65,20},{67,20},{9,19},{37,19},{25,18},{29,18},{35,17},{63,17},{58,16},{64,16},{50,15},{58,15},{40,14},{64,14},{15,13},{16,13},{24,12},{48,12},{27,11},{41,11},{31,10},{65,10},{5,9},{52,9},{17,8},{48,8},{14,7},{16,7},{10,6},{20,6},{28,5},{62,5},{20,4},{44,4},{41,3},{47,3},{22,2},{28,2},{33,1},{42,1},{34,0},{39,0}};​​​​nicegrid[{p72,72}]
Out[]=
There are no lines of 3.
In[]:=
ResourceFunction["FindExtraordinaryLines"][p72]
Out[]=
{}
This might be the first case of an unsolved problem getting a major update during a talk about the problem.