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.)
Some Thoughts Sloane says | Comment 4 of 9 |

Putting in 2,8,23 in the integer encyclopedia found this problem is the basis of sequence A072842 

With four colors, the longest sequence is goes to 66 and with five the longest is 196


  Posted by Brian Smith on 2009-10-14 20:59:44
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 (10)
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