Question 29
Let $n$ be a positive integer. A grasshopper stands on the number line at the number $1$ and may make either a jump of length $2$ or of length $3$ each time. Each time, the grasshopper must land on an integer from $1$ through $n$ where the grasshopper has not been before. The grasshopper would like to visit all integers from $1$ through $n$ exactly once and land on the number $n$.
Prove that this can be done for all $n \ge 9$.
Prove that this can be done for all $n \ge 9$.