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 No Monochrome Sums (Posted on 2009-10-14)
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?

 See The Solution Submitted by Jer No Rating

 Subject Author Date C program Brian Smith 2009-10-15 15:30:45 re(4): Sloane says Charlie 2009-10-15 14:21:37 re(3): Sloane says Charlie 2009-10-15 12:24:52 re(2): Sloane says Charlie 2009-10-15 12:15:53 re: Sloane says Jer 2009-10-15 00:18:25 Sloane says Brian Smith 2009-10-14 20:59:44 Greens to the Party ed bottemiller 2009-10-14 15:13:59 computer solution Charlie 2009-10-14 15:09:47 BRRRRRRRRRRRRRRRR it's cold out ed bottemiller 2009-10-14 14:46:42

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