Given the numbers 2, 4, 8, 10, 14 and 16, $$a \% b$$ is defined as the remainder when the ordinary product $$a \cdot b$$ is divided by 18. Find the % product of every pair of these numbers, including the product of a number with itself, and fill in the table given below.
(1) Find $$2\%2\%2\%...\%2$$, where we find the % product of fifteen 2s.
(2) Find $$8\%8\%8\%...\%8$$ where we have ten 8s.

Repeatedly applying the % operation to 2 cycles through the values $$4, 8, 16, 14, 10, 2$$ before repeating, a cycle of length 6; since $$15 \bmod 6 = 3$$, the result after fifteen 2s lands on the third value in the cycle, which is 8. Repeatedly applying % to 8 cycles through $$10, 8$$ with period 2; since ten is even, the result after ten 8s returns to the second value in the cycle, which is 10.