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?
By expanding the color palate to Red, Blue, and Green, and again starting with N=9, there are 3150 distinct solutions, the lowest of which is R R B R B B R G G. Perhaps Jer intended some interpretation for N > 9 (e.g. add ABCDEF and look for distinct hexadecimal solutions) but this is not apparent to me from the wording. The same strategy/coding would work, but with more equations to test.
Greens to the Party
