2010 AMC 8 Problems/Problem 25
Problem
Everyday at school, Jo climbs a flight of 
stairs. Jo can take the stairs 
, 
, or 
at a time. For example, Jo could climb , then , then . In how many ways can Jo climb the stairs?
Solution 1
A dynamics programming approach is quick and easy. The number of ways to climb one stair is . There are ways to climb two stairs: , or . For 3 stairs, there are 
ways:
(,,)
(,)
(,)
()
For four stairs, consider what step they came from to land on the fourth stair. They could have hopped straight from the 1st, done a double from #2, or used a single step from #3. The ways to get to each of these steps are 
ways to get to step 4. The pattern can then be extended:
steps: ways.
steps: 
ways.
steps: 
ways.
Thus, there are 
ways to get to step 
Video Solution by OmegaLearn
https://youtu.be/5UojVH4Cqqs?t=4560
~ pi_is_3.14
Video by MathTalks
See Also
| 2010 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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