Actually it's quite easy to bruteforce by hand if you mention that point set has multiple symmetries. For example, you only need to start drawing lines from (0,

Actually it's quite easy to bruteforce by hand if you mention that point set has multiple symmetries. For example, you only need to start drawing lines from (0,0), (0,1) and (1,1). Any other combinations are derived by rotation and mirroring. After several minutes you can prove that solution in impossible under implicit presumption that every line must terminate at a dot. And after that puzzle is really easy.