In mathematics, square packing is a classic geometric optimization problem: what is the smallest container square of side length $W$ that can contain $N$ unit squares without overlapping?
For square counts like $N=1, 4, 9, 16$, the optimal packing is a straightforward axis-aligned grid ($1\times1, 2\times2, 3\times3, 4\times4$).
Why is 17 Squares Famous?
For $N=17$, packing 17 unit squares inside a standard grid requires a $5 \times 5$ container ($W = 5.0$), leaving space for 8 empty squares! However, in 1998, mathematician John Bidwell discovered that by tilting 7 squares at strange angles ($\sim 39.8^\circ$ and $\sim 53.4^\circ$), all 17 unit squares fit inside a container of side length $W \approx 4.67553$!
This arrangement remains the world record best-known solution today. Remarkably, it is deeply asymmetric, surprising mathematicians who originally expected symmetric solutions!