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) | ||
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