Question 19
A machine processes a natural number as follows. If the number is even, it divides it by 2. If the number is odd, it subtracts 1. It repeats these steps until the result is 0, then stops. How many starting numbers reach 0 in exactly 6 steps?
For example, there are two starting numbers that take exactly 3 steps: 3 and 4.
$3→2→1→0$ (3 steps)
$4→2→1→0$ (3 steps)
For example, there are two starting numbers that take exactly 3 steps: 3 and 4.
$3→2→1→0$ (3 steps)
$4→2→1→0$ (3 steps)