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?

(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