A 10x10 square can obviously hold 100 unit circles (diameter=1) when arranged in rows and columns. What is the maximum number of non-overlapping unit circles a 10x10 square can hold if the circles are packed closer together?

Answer:105.

first row, 1 unit. Second row equals 2*(.5-(��(.75)))=.732051... in length, third row 1, fourth .732051... and so on, so you can fit 11 rows of circles instead of 10. However, the first row fits 10 circles, but the second only nine. The third, 10, the fourth, 9, and so on. After adding up the number of circles per row, you end up with 105 circles total.

Edited on July 30, 2004, 11:24 am

Posted by Henry on 2004-07-29 17:38:32