The Proof is Trivial!

I noticed that the mathematics forum is currently lacking a thread where people can post interesting and challenging problems for fellow mathematicians to ponder, so here it is.

Please don't post here for queries on A level or STEP questions, as they each have their respective threads. The level of the questions can of course vary, but they should be fun, interesting, and most importantly solvable! Please don't post questions that you're not able or willing to provide solutions to. Questions that require knowledge of graduate level theorems won't be of interest to most of us, so keep the level reasonable.

http://www.thestudentroom.co.uk/showthread.php?t=2313384