He said there was one puzzle he liked, but he couldn't remember how it went. While we were riding the lift up, I asked my Dad if he knew of any puzzles. They were hard to get used to at first because it felt like they had more traction or something, but it was fun. He had bought a new pair of skiis and handed me down his old ones. The Puzzle of Squares Given six identical squares where any group of five have exactly two common points, does there exist a common point for all six? I'll give you guys a chance to post your own solutions to these problems in the comments (although I've never gotten a comment on any of these posts before, so I don't know who I'm addressing). It's very similar to the one above, but there are a few more nuances that you have to deal with. It's like saying, 'See? I told you it wouldn't work out.' You assume the exact opposite of what you want to prove and then derive a false conclusion. If you're not familiar with it already, it's a cool trick. The above solution uses a logical maneuver called proof by contradiction (or to be more specific, contrapositive). Therefore, the five circles must have a common point.

However, circles can obviously only intersect at up to two distinct points (like in a Venn Diagram). This tells us that circles A and B share at least three distinct points: C', D', and E'.

If we assume that there isn't a common point for all five circles, we know that A', B', C', D', and E' must be distinct. Let's say that A' is a common point shared by all the circles except circle A, B' is a common point shared by all the circles except circle B, and so on. You can try to solve the problem on your own before reading on. As you'll soon see, you don't need advanced knowledge of math or geometry to solve these types of problems - though it does help to come equipped with a methodical way of thinking and good intuition. Hopefully, this and the solution below will serve as adequate introduction.

Hexcells plus chance