I've just watched the calmly titled "The 15-game" in the Numberphile Youtube channel and boy oh boy, I cannot stop thinking about it!

I will not spoil the end, but if you ever got intrigued by games, maths, brain-teasers, just take a 15-minute break and watch it. At school, I loved to solve the same problem from different angles, not only to increase my chances of getting the good answer, but also because it was fun. This video hit right there in my heart.
One of my first programs was a game of tic-tac-toe. If only someone had shown me the 15-game back then!
I choose 5. Your turn!