This is a challenge !!!!!
There are three objects, A, B, and C, and an operation called “doesn’t have a name”.
Two are similar, and the third is a bit different
They are paired to yield a single object as follows:
AA = BB = CC = C
AB = BC = CA = B
AC = CB = BA = A
Notice that BC and CB are different, so non-abelian.
Worse is that (AC)A = C and A(CA) = B are different, so non-associative.
And consequently A and B and C are different.
Your job is to identify (model, in current jargon) the objects and the operation.”
The next post will be “the solution”.