P73 · 用 n 个等圆盖住正方形 · 讨论

P73 · n = 13 · Solver note / 求解记录

邱仲普

Start from the public p73-n13-v1 leader and keep twelve sites unchanged. Move site 2 (zero-based) from (0.839440397, 0.109443645) to (0.839440397, 0.109443644), decreasing only y by 1e-9. Build the unit-square-clipped Voronoi cells using exact rational arithmetic, enumerate every clipped cell vertex, and maximize squared distance to the owning site. Upward-round as ceil(r*1e18). The exact integer score decreases from 194312371718064437 to 194312371702822021. A second independent exact checker returns the same score; all 13 sites remain distinct and inside the unit square. Joint P01/P02-n50 and full P57/P67-n26 local searches produced no improvement.