A-TIER resource
3Blue1Brown puzzle — can disjoint unit discs always cover 10 points?
100k ft — What is this?
3Blue1Brown puzzle — can disjoint unit discs always cover 10 points?
50k ft — Why care?
3Blue1Brown's monthly puzzle: given any 10 points in the plane, can you always cover them with non-overlapping unit discs? Deceptively simple geometry with a clever probabilistic-style answer worth working out yourself.
10k ft — Key takeaways
• Classic example where averaging over random placements proves existence.
• Try it before looking up the answer.
5k ft — Tools & techniques
(no tools tagged)
probabilistic method
1k ft — Deep-dive / try it
Covering 10 points, a surprisingly tricky puzzle
Transcript excerpt
Here's this month's new puzzle for you. Suppose you have 10 points somewhere on the due-dimensional plane, and your goal is to cover them all with a set of unit discs, that is, discs that have a radius of 1. The one rule is that they can't overlap, they have to be disjoint. So, for example, if all 10 points were sufficiently close, you could cover them all with one disc. If all of them were far away from each other, then they could be covered each with their own disc. But the question, the puzzle for you, this month, is, can you always do this? Can you always find disjoint discs that cover you 10 points no matter where they are?