2-by-n Disk-Packing Paradox

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details

The top box shows that it is easy to place

2n

unit diameter disks in a

2×n

rectangle, namely by fitting two disks at a time side by side.

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

n

.

It is therefore surprising that if

n

is sufficiently large more disks can be packed.

The lower rectangle shows how a

2×164

rectangle can be filled with 329 unit disks.

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