Covering 10 points, a surprisingly tricky puzzle.

0:00 Here's this month's new puzzle for you.

0:01 Suppose you have 10 points somewhere on the two-dimensional plane,

0:04 and your goal is to cover them all with a set of unit discs,

0:07 that is, discs that have a radius of one.

0:10 The one rule is that they can't overlap.

0:11 They have to be disjoint.

0:13 So, for example, if all 10 points were sufficiently close,

0:16 you could cover them all with one disc.

0:17 If all of them were far away from each other,

0:19 then they could be covered each with their own disc.

0:22 But the question, the puzzle for you this month, is can you always do this?

0:26 Can you always find disjoint discs that cover your 10 points,

0:30 no matter where they are?