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Can you paint every number from 1 to 8 with two colours, such that there are no distinct numbers $a, b, c$ of the same colour with $a+b=c$? For example, you cannot have 2, 3 and 5 of the same colour since $2+3=5$.

Good luck!

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How about this

Red - $\{1,2,4,8\}$
Blue - $\{3,5,6,7\}$

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  • $\begingroup$ Correct! Well done. $\endgroup$ – Dmitry Kamenetsky Oct 18 at 11:30

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