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# Counting

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How many two-digit numbers are there such that the two digits differ by exactly \(3\)?

Jan 31, 2022

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The possible pairs of numbers are \((0,3), (1,4), (2,5), (3,6) ,(4, 7),(5,8),(6,9)\)

Each of the \(7\) pairs can be ordered in \(2\) ways, making for \(14 \) numbers.

However, we need to account for the fact that the number \(03\) is not a \(2\)-digit number, so we have to subtract \(1\), making our total \(\color{brown}\boxed{13}\)

Jan 31, 2022