# 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.

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