I've been going through this representation theory lecture notes, and I've found the ''hungry knights'' problem very interesting. Do you know any interesting problems similar to that one?
To define ''similar'': problems which have a recreational, puzzle-like taste and you can solve them using representation theory/group theory. One example I know is this series of blog posts by Qiaochu Yuan applying group theory to few basic combinatorial questions about colorings.
A similar one is a Russian Olympiad problem about 7 dwarfs sitting around a table drinking wine. Each of them have a wine cup in front of them. In turn, they split the wine in their glass into 6 equal portions and distribute it out. After a round of distribution, they found that they have the same amount of wine as at the start. How much wine did each dwarf have?