I was able to quickly come up with a pattern to find all 27 combonations of the shapes. What I did struggle with was actually writing down, in an understandable way, the rules for which I found the pattern. I believe my students will struggle with that as well. I think they will have something that makes sense to the two partners, but not everyone else will understand.
A point of the activity is that different rules can exist. The number systems we know and love are often treated as mathematical “fact” but are abstractions invented by humans. What if our hands had 8 fingers instead of 10?
Similarly our counting system which works like and odometer - cycle through all of the digits in the 1’s place, increment the digit in the 10s place, and so on - is also arbitrary. It’s an easy rule to follow, but also man-made. There are examples of number systems used throughout human history both with different bases (e.g. base 5 and base 20) as well as different counting systems (see: roman numerals).