
3. Felix chooses a positive integer as the starting number and writes it on the board. He then repeats the next step: he replaces the number $n$ on the board by $\frac{1}{2} n$ if $n$ is even and by $n^{2}+3$ if $n$ is odd.

For how many choices of starting numbers below 2023 will Felix never write a number of more than four digits on the board?

## 3. Version for klas $5 \&$ klas 6

In the solution for klas 4 and below, the question is solved in two parts. In part (a), we show that if Felix starts with an odd number, the next two numbers he writes down will be even. In part (b) we show that the number after that will be odd, from which we deduce that there are 21 starting numbers below 2023 where Felix will never write a number of more than four digits on the board.

