Less than a million and divisible by three

Discrete Mathematics Level 5

Let us call \(n \in \mathbb{N}\) good if all the digits of \(n\) are odd and \(n\) is divisible by \(3\). How many good \(n<10^6\) exist?

Details and Assumptions:

  • Here, we talk about \(n\) in its base \(10\) representation.

  • \(\mathbb{N}\) is the set of natural numbers.


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