The 15-game blew my mind

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…