I'm trying to find puzzles that introduces a new operator by giving a few examples and asks for a computation at the end. An example would be 5 & 3 = 3, 8 & 2 = 4, compute 6 & 2. Have anyone seen or done any similar problems?
I haven't seen one myself, but your example may inspire one which I'll explain.
There's clock arithmetic where, e.g., you can have 10 + 4 = 2 or 11 + 3 = 2 so instead of a plus sign, you might adapt the face of a clock in place of that symbol.