# Getting to 1653

**Discrete Mathematics**Level pending

You start with \(0\).

Then, as many times as you like, you can choose to perform one the following operations: \(+1\), \(\times 2\), or \(\times 3\)

What is the fewest number of operations you would need to perform to get to \(1653\)?

For example, you could get to \(54\) with the following operations:

\(0 \rightarrow +1 \rightarrow \times 3 \rightarrow \times 3 \rightarrow \times 3 \rightarrow \times 2\)

And, that would be considered \(5\) operations.