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

Home > Numbers
No Monochrome Sums (Posted on 2009-10-14) Difficulty: 3 of 5
Color each of the numbers 1 through n either red or blue such that if a+b=c then a, b and c are not all the same color. The addends are distinct.

For example with n=6 the sequence rbrbrb does not work because 2+4=6 but are all blue. Whereas rbrbbr does work.

What is the largest value of n for which such a sequence exists?

Note: Since the colors can be swapped, make the number 1 red.

Add a third color (green.) What is the new maximum value of n?

See The Solution Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Sloane says | Comment 5 of 9 |
(In reply to Sloane says by Brian Smith)

Thanks for the link.  I had found a 3 color solution with n=23 but didn't know if it was maximal. 

Charlie, how fast is your program?  I wonder if it can do 5 colors...

  Posted by Jer on 2009-10-15 00:18:25

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 (4)
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