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.

  Submitted by Ady TZIDON    
No Rating
Solution: (Hide)
The replacement operation preserves the parity of the sum, so the last number left cannot be even.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Gilding the LilySteve Herman2013-12-13 10:07:21
re(5): All things being equal ... (spoiler)Ady TZIDON2013-12-13 02:08:02
re(4): All things being equal ... (spoiler)Ady TZIDON2013-12-13 02:04:50
re(4): All things being equal ... (spoiler)Charlie2013-12-13 01:54:49
re(3): All things being equal ... (spoiler)xdog2013-12-12 18:19:21
re(2): All things being equal ... (spoiler)Charlie2013-12-12 11:13:20
re: All things being equal ... (spoiler)xdog2013-12-12 10:58:22
SolutionAll things being equal ... (spoiler)Steve Herman2013-12-12 10:02:57
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 (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information