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?
Assuming N is limited to 9, I tested in reverse. For N=9 I found no solution, but for N=8 there was exactly one (assuming that 1 is always red) -- R R B R B B B R.
For N=9, there are 16 equations all of which must satisfy the condition that a+b=c with no three-color match for some set of assignments; no set worked. For N=8, there are 12 equations all of which must satisfy the conditiont. The set above works. I did not repeat for N < 8.
If I have time, I will recode to try the three color version.
BRRRRRRRRRRRRRRRR it's cold out
