Question 10
Consider the following operation. Given a positive integer $n,$ if $n$ is a multiple of $3,$ then you replace $n$ by $\tfrac{n}{3}.$ If $n$ is not a multiple of $3,$ then you replace $n$ by $n + 10.$ Then continue this process. For example, beginning with $n = 4,$ this procedure gives $4 \to 14 \to 24 \to 8$ $\to 18 \to 6 \to 2 \to 12 \to \cdots.$
Suppose you start with $n = 100.$ What value results if you perform this operation exactly $100$ times?
Suppose you start with $n = 100.$ What value results if you perform this operation exactly $100$ times?