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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