Assignment #2, Question 4

Here we are asked to find how many possible binary operations there are if we are working in trinary.

Recall that when we were working in binary, we ended up having 16 binary operations, where each of the binary operations could be represented by a unique 4-tuple composed of either 0s or 1s.

Thus, by the multiplication principle, we get 2x2x2x2=16 operations.

Applying this to trinary.

We see that each binary operation, in trinary, can be represented by a unique 9-tuple composed of either 0s, 1s, or 2s.

Again, apply the multiplication principle and we get 3x3x3x3x3x3x3x3x3 = 3^9 possible operations.