perplexus.info :: Numbers : No Monochrome Sums

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?

Submitted by Jer

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Solution: (Hide)

The longest with two colors is n=8:
rrbrbbbr
With 3 colors I have found a solution with n=23:
rrbrbbbrggrggggrggbgbrb
See the comments for other solutions.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-08-11 22:48:00
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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