A New Lower Bound for Packing 17 Unit Squares
Another better lower bound for n=17 square packing
Gustavo Massaccesi improves the lower bound for packing 17 unit squares into a larger square, proving s(17) ≥ 4.5058. Building on recent work by Sam Burns, he uses linear programming to find optimal weight distributions, reducing the gap between known lower and upper bounds. The result, verified by a rational arithmetic program, also improves bounds for s(18), s(19), and s(20).
So if we try to fit 17 unit squares there, at least two unit squares must share one of the 16 interesting points.