Thumbnail for Covering 10 points, a surprisingly tricky puzzle. by 3Blue1Brown

Covering 10 points, a surprisingly tricky puzzle.

3Blue1Brown

28s122 words~1 min read
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[0:00]Suppose you have 10 points somewhere on the two-dimensional plane and your goal is to cover them all with a set of unit discs, that is discs that have a radius of one.
[0:13]So, for example, if all 10 points were sufficiently close, you could cover them all with one disc.
[0:19]If all of them were far away from each other, then they could be covered each with their own disc.
[0:27]Can you always find disjoint discs that cover your 10 points, no matter where they are.
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[0:00]Here's this month's new puzzle for you. Suppose you have 10 points somewhere on the two-dimensional plane and your goal is to cover them all with a set of unit discs, that is discs that have a radius of one.

[0:10]The one rule is that they can't overlap, they have to be disjoint.

[0:13]So, for example, if all 10 points were sufficiently close, you could cover them all with one disc.

[0:19]If all of them were far away from each other, then they could be covered each with their own disc.

[0:23]But the question, the puzzle for you this month is can you always do this?

[0:27]Can you always find disjoint discs that cover your 10 points, no matter where they are.

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