You start with the number 3 on the board. Each time you can replace the number x that is written on the board with either one of the following numbers: 5x+8, 4x+6, 2x+2. What is the lowest number of steps you can do to reach the number 9999998?
I tried to start both from the start (with the greedy method) and from the end but had no success. A hint for the solution would be amazing!