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

Home > Numbers
Last but not the least (Posted on 2013-12-12) Difficulty: 2 of 5
Numbers 1, 2, 3, ... 2014 are written on a board.
You are allowed to replace any two of these numbers by a new number, which is either the sum or the difference of these numbers.

Show that after 2013 times performing this operation, the only number left on the board cannot be zero.

See The Solution Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Gilding the Lily Comment 8 of 8 |
The last number remaining after 2013 operations can be any ODD number that is not greater than 2,029,105 (the sum of all the terms) and not less than -2,029,103 (i.e., 1 minus the sum of the last 2013 terms).  Thus, it can be any of 2,029,105 values, all ODD.  
  Posted by Steve Herman on 2013-12-13 10:07:21
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information