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