Place n equal squares in the unit square, each free to tilt, none overlapping, and make their common side as large as possible.
Formal definition
ContainerThe unit square: the origin (0, 0) at its lower-left corner, (1, 1) at its upper right
SubmissionEach square is {cx, cy, ux, uy}: a centre plus one half-edge vector, the other fixed as (−uy, ux)
ConstraintsEvery square tilts freely; all lie inside the container; no two overlap in their interiors, touching allowed. Only the smallest square is scored, so unequal sides gain nothing
ObjectiveMake the common side as large as possible; compared internally by its square, exactly
Getting a feel for it
Why tilting is the point
Straight is a grid; tilting squeezes space out of the seams a grid leaves — the best known n = 5 has one square at 45° wedged between four straight ones. Tilting is the entire difference between this and plain packing.
Where the frontier is
The classic s(n) problem: proven for n = 3, 4, 6..9, 14..16 and 25 (Göbel, Kearney–Shiu and others), the rest open; Friedman's squares survey keeps the running record.