Can you always cover 10 points with 10 equally sized (non-overlapping) coins?

The video tutorial explores the problem of covering points on a plane with non-overlapping coins, emphasizing that it's always possible to cover 10 points with 10 coins. It discusses the limitations of this coverage for larger numbers of points and introduces the concept of hexagonal lattice packing density. The tutorial uses probability and expected values to demonstrate the coverage solution, highlighting the linearity of expectation as a key principle.

What does the author mean by saying that the proof is not obvious?

Describe the relationship between the average number of points covered and the expected number of points covered when tossing the lattice.

What is the significance of the linearity of expectation in the proof of covering points with coins?