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.)
re(3): A new approach with no proof | Comment 7 of 24 |
(In reply to re(2): A new approach with no proof by friedlinguini)

If you consider a flat hallway to be a "stairwell" with zero steps (as I did in my listing, then you do have the first "1" as well, but it still results in the 101st Fibonacci number being associated with 100 steps.

I did a search for Fibonacci and found the following page: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpuzzles.html

It has a number of puzzles which are clearly variant "word problem" clothing for two or three Number Theory problems invoving Fibonacci numbers. The generic version of this starwell problem is included, and the following are the same problem in other clothing: Bee-Line; Chairs, No Neighboring Teachers; Stepping stones; Leonardo's Lane.

Anyway, this confirms that we have found the correct answer.
  Posted by TomM on 2002-09-06 06:28:58

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


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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