Equal discs covering a disc · n = 19
Cover the largest possible disc with n unit-radius discs. Maximise the covered disc radius.
Instancen = 19
ObjectiveMaximize covered disc radius
Record comparison
covered disc radius · Higher is better| Record | Value / interval | Author / holder | Source |
|---|---|---|---|
| Proven optimum | √13 | VonEquinox | DiskCoveringSolve ↗ |
| Site record | No player record yet | — | — |
The continuous optimum is proved, so competition submissions are closed. Historical records and contribution points are retained. Because finite-decimal coordinates cannot attain this value exactly, the current certificate is not claimed optimal on the nine-decimal grid.
Formal definition
- ContainerThe editor and certificate normalise the target disc to the closed unit disc centred at (1,1), while public scores are reported in the literature's unit-covering-disc scale.
- SubmissionSubmit {radius, placements:[{x,y,turn},…]}, with each value written as a decimal string of at most nine places. Here x, y are centre coordinates; circles require turn = 0 and polygons use turn = tan(θ/2). Coordinates and turn must lie in [−4, 4], with 0 < radius ≤ 4.
- ConstraintsThe n distinct centres lie inside the target disc. Covering discs may overlap and protrude, and their union must cover every point of the target disc.
- PrecisionInput decimals are parsed as exact rationals, with zero floating-point tolerance in feasibility checks.
- ObjectiveCovered disc radius R = 1/r, where larger is better.
