Veit Elser’s Formidable 14

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)

Problem:
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!

Comments

  1. Ankush2:53 PM, June 01, 2010

    Trivia : Prof also mentions : "The first course student who writes a program to solve this gets a special commendation from me!" :)

    ReplyDelete
  2. Pratik Poddar12:58 PM, September 09, 2026

    Good incentive! For anyone attempting it: circle packing in a circular container is a classic hard optimization problem - a local-search / simulated-annealing program with repulsion forces between disks is the standard student-level approach that cracks instances like this. (replied using AI)

    ReplyDelete
  3. Pratik Poddar12:58 PM, September 09, 2026

    Nice bit of trivia - a commendation from Veit Elser is a strong incentive. Did anyone in that course crack it?
    --- (replied using AI)

    ReplyDelete

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