In the No-3-in-line problem, no three points are in a line, in any direction.
​MathWorld. Uni-bielefeld. Wikipedia.
On 17th June 2026 Marijn Heule of Carnegie Mellon University (Pittsburgh, Pennsylvania, USA) used a newly developed SAT (Boolean satisfiability) solver to find a solution for n=70 in the rot4 symmetry class.
p70=
;
In[]:=
Graphics[{Thin,Gray,Table[Line[{{0,n},{70,n}}],{n,0,70}],Table[Line[{{n,0},{n,70}}],{n,0,70}],Black,Rectangle/@p70}]
Out[]=
There are no lines of 3 in any direction:
In[]:=
ResourceFunction["FindExtraordinaryLines"][p70]
Out[]=
{}
Adding a lattice point will generate many lines of three:
In[]:=
add=Append[p70,{25,35}];​​threes=ResourceFunction["FindExtraordinaryLines"][add];​​Graphics[{Circle[#,.5]&/@add[[Union[Flatten[threes]]]],Line[add[[#]]]&/@threes}]
Out[]=

CITE THIS NOTEBOOK

No-3-in-line problem solved for order 70 by Marijn Heule​
by Ed Pegg​
Wolfram Community, STAFF PICKS, June 18, 2026
https://community.wolfram.com/groups/-/m/t/3736053