# 2-by-n Disk-Packing Paradox

2-by-n Disk-Packing Paradox

The top box shows that it is easy to place unit diameter disks in a rectangle, namely by fitting two disks at a time side by side.

2n

2×n

At first glance this seems to be the best possible for any .

n

It is therefore surprising that if is sufficiently large more disks can be packed.

n

The lower rectangle shows how a rectangle can be filled with 329 unit disks.

2×164

There are seven disks at each end and 105 sets of three disks in the middle.