Source: CMU Spring 2010 Course on Great Theoretical Ideas in Computer Science Lecture01. Course pointed to me by Aaditya Ramdas (To be CMU Grad Student & CSE-IITB Alumnus)
Fit disks of the following diameters into a circular cavity of size 12.000:
2.150 2.250 2.308 2.348 2.586 2.684 2.684
2.964 2.986 3.194 3.320 3.414 3.670 3.736
Write a program or give a general algorithm to solve a general case.
Disclaimer: Did not spend a lot of time on the problem but I have not been able to solve it. Clearly sum of the squares of the smaller radii is less than the square of the larger radii suggesting that it might be possible to fit disks. I am not able to make any more comments!