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

Home > Just Math
Where Did You Start? (Posted on 2017-11-16) Difficulty: 3 of 5
2015 pieces of stones are placed to form a circle. They are numbered with 1,2,3,4,...,2015 clockwise. Starting from somewhere, you remove a stone. Then going clockwise, you remove every other stone, one at a time. Finally, there is only stone left, and that stone is 2014. What was the first stone you removed?

No Solution Yet Submitted by chun    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution My approach Comment 3 of 3 |
By starting with 1 and with different numbers of stones a pattern emerges:

If the number of stones is 2^n then the last stone will be 2^n.
For every stone short of a power of 2, the last stone drops by 2.

(For 2^n - a, if a<2^(n-1), the last stone is 2^n - 2a)
2015 is 33 short of 2048=2^11.
2048 - 2*33 = 1982.

For 2015 stones, if you start with 1, you end with 1982.
Now just shift this by 2014-1982=32 places and start instead with

  Posted by Jer on 2017-11-17 07:34:50
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 (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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