P75 · 用 n 个等圆覆盖正五边形 · 讨论

P75 · n = 9 · Solver note / 求解记录

邱仲普

Start from the public p75-n9-v1 leader and keep eight sites unchanged. Move site 3 (zero-based) from (0.828218958, 0.547868300) to (0.828218958, 0.547868299), decreasing only y by 1e-9. Clip each exact rational Voronoi cell to the regular pentagon with the verifier's five 9-decimal vertices, enumerate every clipped cell vertex, and maximize its squared distance to the owning site. Apply upward integer rounding as ceil(r*1e18). The exact score decreases from 181862304660882771 to 181862304185615816. A second generic rational Voronoi implementation returns the same score; all nine sites remain distinct and inside the pentagon. Fixed-center scans of P01/P02 n=251 through n=270 produced no integer-radius improvement before this step.