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Counting steps brainteaser

By David, 13 April 2022 Brainteaser

Difficulty: Tricky

Willow has a staircase with 7 steps. She likes to walk down the staircase in different ways. Sometimes she takes 1 step at a time, and other times she skips a step and goes 2 at a time. If Willow mixes up these 2 types of steps, how many different ways can she walk down the stairs?
 
Scroll down or click for a hint, or the answer!

 

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Brainteaser hint

Try breaking it down step by step. How many ways are there to get to the first step? How about the second step?

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Brainteaser answer

There’s only 1 way Willow can get to the first step. There are 2 different ways she could get to the second step – she could step from the first, or skip the first and go there straight away.

Willow could get to the third step from either the first or the second step. Since there is 1 way to get to the first step, and 2 ways to get to the second step, there must be 1 + 2 = 3 ways to get to the third step.

We can continue this pattern. To get to the fourth step, Willow can come from the second or third steps, and 2 + 3 = 5.

There are then 3 + 5 = 8 ways of getting to the fifth step, 5 + 8 = 13 ways of getting to the sixth, and 8 + 13 = 21 ways of getting to the seventh and final step. So the answer is 21!

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