# 1, 2 buckle my shoe

How many ordered sets of digits $$(a, b)$$ are there, such that the number $$\overline {1ab2}$$ is a multiple of 3?

Details and assumptions

Digits are integers from 0 to 9 inclusive.

The notation $$\overline{abc}$$ denotes $$100a + 10b + 1c$$, as opposed to $$a \times b \times c$$. As an explicit example, for $$a=2, b=3, c=4$$, $$\overline{abc} = 234$$ and not $$2 \times 3 \times 4 = 24$$.

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