Distinct Digits Function

Algebra Level pending

The function \(\text{dd}(n)\) takes in a positive integer \(n\), and gives the number of distinct digits in \(n\), when written in base 10.

How many elements are there in the range of \(\text{dd}(n)\)?

As an explicit example, \(\text{dd}(1123) = 3\), since there are three distinct digits in 1123, namely 1, 2, and 3.

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