Going up stairs as shown in a figure by 1 or 2 stairs at a time in one step.
For example, when going up to the 3rd step, there are 3 ways of
1 stair - 1 stair - 1 stair,
1 stair - 2 stairs,
2 stairs - 1 stair.
Answer the following questions.
(1) When going up to the 5th stairs, how many ways of going up are there?
(2) When going up to the 10th stairs, how many ways of going up are there?
Answer
(1) 8 ways
(2) 89 ways
Solution
(1) The number of way of going up to the 1st stair is one.
The number of way of going up to the 2nd stair is two of 1 stair - 1 stair and 2 stairs.
The number of way of going up to the 3rd stair is three.
Since it is from the 2nd stair or the 3rd stair to go up to the 4th stair, the number of way of going up to the 4th stair is 2 + 3 = 5.
The number of way of going up to the 5th stair is to be 3 + 5 = 8 by thinking the same way.
(2) Based on the view of (1), the number of ways of going up is arranged as shown in a table below.
The number of way of going up to the 10th stair is 34 + 55 = 89.
For example, when going up to the 3rd step, there are 3 ways of
1 stair - 1 stair - 1 stair,
1 stair - 2 stairs,
2 stairs - 1 stair.
Answer the following questions.
(1) When going up to the 5th stairs, how many ways of going up are there?
(2) When going up to the 10th stairs, how many ways of going up are there?
Answer
(1) 8 ways
(2) 89 ways
Solution
(1) The number of way of going up to the 1st stair is one.
The number of way of going up to the 2nd stair is two of 1 stair - 1 stair and 2 stairs.
The number of way of going up to the 3rd stair is three.
Since it is from the 2nd stair or the 3rd stair to go up to the 4th stair, the number of way of going up to the 4th stair is 2 + 3 = 5.
The number of way of going up to the 5th stair is to be 3 + 5 = 8 by thinking the same way.
(2) Based on the view of (1), the number of ways of going up is arranged as shown in a table below.
The number of way of going up to the 10th stair is 34 + 55 = 89.
