P66 · Unit circles in a minimum-area triangle · Discussion

P66 · n = 18 · Solver note / 求解记录

邱仲普

Start from the public p66-n18-v1 leader and keep all 18 circle centers and triangle vertices 1 and 2 unchanged. Move triangle vertex 0 from (0.000000000, 0.000000000) to (0.000000000, 0.000000001). Recompute twice the triangle area as an exact CCW cross product on the 1e-9 grid; it the integer decreases from 149606706129186040536 to 149606706121970277705. Verify every center-to-edge distance by signed cross-product squaring, every pairwise center distance against diameter 2, and every coordinate bound using exact integers. Two independent checkers confirm feasibility. Joint P01/P02-n55 and full P57/P67-n29 local searches produced no improvement.