Al Zimmermann is running a programming competition to see who can:

Pack

nnon-overlapping circles with radii from 1 toninto as small a circle as possible.

You have until mid-January to come up with solutions for *n* between 5 and 50.

*(via Lamba the Ultimate).*

I’m having a lot of trouble understanding the rules:

What does “No circles must be concentric (that is: they share the same center).” mean? That no pair of circles should be concentric is trivially obvious and not a very interesting constraint because there are many ways to not have a packing that don’t involve concentric circles.

What does “Coordinates can have 20 digits, and the scorer scales them in order to avoid collisions into your submitted set.” mean? I’d have thought that the scorer shouldn’t tamper with your submission.

What could “the scorer will compute the smallest circumscribing circle, by automatically scaling your input” possibly mean? I don’t see why you have to scale anything to compute the smallest circumscribing circle.

And why the bizarre scoring formula?

There are some eccentricities in the contest …

I don’t understand the “No circles must be concentric” rule either. I came to the same conclusion as you and then dismissed it as harmless noise.

I suspect the scaling is to allow you to use integer arithmetic and submit integer entries. Though, they really ought to have made people do their own scaling first (to avoid confusion).

As for the scoring formula … I guess the goal was to come up with something that was continuous, monotonic, and had a bonus for the best score.

Some of your questions may also be answered by the FAQ. And there is also a discussion forum.

… just had a look at the forum, and it turns out there is a reason for the “No circles must be concentric”.

There are some eccentricities in the contest â€¦Nice pun!