Another Brain Teaser

So the answer to the brain teaser is 0.5. Isn’t that an interesting result? I thought so.

Here’s another one. Say you have a table, and on the table are a bunch of quarters arranged such that if you were to place an additional quarter anywhere on the table, it would overlap with at least one quarter already on the table. In other words, there’s no circular area of clear space on the table as large as or larger than the area of a quarter.

Say the number of quarters on the table is X. Using a simple, one sentence explanation, prove that with 4X quarters you could cover the entire table so that no table is showing – it’s completely covered by quarter.