AMO 2027 Grades 9-11 SET 4 - Self-study Question 6

A cricket climbs a staircase by leaping either 1 step or 2 steps upward with each bound. In how many different ways can it climb a 9-step staircase? For example, a 3-step staircase has exactly three ways: $1+1+1$, $1+2$, and $2+1$.

Enter one positive integer, without units.