Question

Everyday at school, Jo climbs a flight of 66 stairs. Jo can take the stairs 11, 22, or 33 at a time. For example, Jo could climb 33, then 11, then 22. In how many ways can Jo climb the stairs

Answer 1

Answer: There are 24 ways.

Step-by-step explanation:

All the numbers are divisible by 11, so divide all the numbers by 11 to make the problem simpler: Jo climbs a flight of 6 stairs. Jo can take the stairs 1, 2, or 3 at a time.

A recursive approach can now solve this problem. The number of ways to climb one stair is 1. There are two ways to climb 2 stairs: (1, 1) or (2). For 3 stairs, there are 4 ways: (1, 1, 1), (1, 2), (2, 1), and (3). Extending this pattern, there are 1+2+4 = 7 ways to climb up 4 stairs, 2+4+7 = 13 ways to climb up 5 stairs, and 4+7+13 = 24 ways to get up 6 stairs.