All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Climbing the stairs (Posted on 2002-09-05) Difficulty: 3 of 5
A stairway has 100 steps. You can climb it by one step at a time, or by two steps. How many different ways to ascend this stairway exist?

See The Solution Submitted by levik    
Rating: 3.3333 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips A new approach with no proof | Comment 3 of 24 |
(In reply to Limit by TomM)

I decided to generalize the problem, solve it for some smaller numbers of steps and see if there was a pattern.

This is what I found:

0 steps -> 1 set
1 step -> 1 set
2 steps -> 2 sets
3 steps -> 3 sets
4 steps -> 5 sets
5 steps -> 8 sets

This sequence is awfully familiar: it is the Fibonacci sequence (It does turn up in the strangest places.) If this holds up, then the number of ways to climb the stair, given the restrains is the 101st Fibonacci number (573147844013817084101)
  Posted by TomM on 2002-09-05 19:37:34

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information