Place n circles of one common radius inside a quadrant (quarter-disc) of radius 1, making that radius as large as possible.
Formal definition
ContainerThe container is a quarter-disc of radius 1: centred at the origin (0, 0), with its straight edges along the axes from 0 to 1 and the arc in the first quadrant.
SubmissionExactly n circles: one shared radius and n centres; every circle uses the same radius
ConstraintsEvery circle lies wholly inside the container; no two overlap in their interiors, tangency allowed
ObjectiveMake the common radius as large as possible
Getting a feel for it
Where the room for improvement is
Optimal packings are jammed contact structures: circles brace against each other and the boundary, with tilted rows, offsets, and the odd rattler touching nothing. Neat grids are almost never optimal.
Where the frontier is
The best known values come from Specht's ccq survey table, none proven; all fourteen n are open.