1. [3] Paul starts with the number 19. In one step, he can add 1 to his number, divide his number by 2 , or divide his number by 3 . What is the minimum number of steps Paul needs to get to 1 ?
Answer: 6 One possible path is $19 \rightarrow 20 \rightarrow 10 \rightarrow 5 \rightarrow 6 \rightarrow 2 \rightarrow 1$.