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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

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 Sloane says | Comment 4 of 9 |

Putting in 2,8,23 in the integer encyclopedia found this problem is the basis of sequence A072842

With four colors, the longest sequence is goes to 66 and with five the longest is 196

 Posted by Brian Smith on 2009-10-14 20:59:44

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