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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

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Sloane says | Comment 5 of 9 |
(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

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