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 re(3): Sloane says by Charlie)

The program has gotten up to n=55 for the 4-color:

rrbrbbrggrgbrbgrygrygrbbryyryyrbbryyryyrybrggrggrgbrbyr

Posted by Charlie on 2009-10-15 14:21:37