If you don't know what sandpiles are and you haven't watched Numberphile's video on the topic, here is the Link: https://goo.gl/JVcqEI . If you are all caught up, here is the question:
The set S described in the video is indeed a group (by addition). Can you prove that any set you wish in which you start with a 3x3 sandpile and only include the sandpiles added on is a group? You do not need to prove this for all sets, just one of your choice. If you prove it for all sets, you get bonus points.
(Hint: Find identity sandpile algorithm and inverse sandpile algorithm)
That one guy that's always on