I think there must be a way to solve this but I can't get there

Green + Blue = Yellow

Red + Green = Purple

Yellow - Purple = Red

Red + Green + Blue = 9

I have made some progress

Swap out B so, R + G + Y - G = 9 R + Y = 9


Replace G with the provided formula R + G = P R + Y - B = P (from above) 9 -B = P 9 = P + B

but I run out of steam from then...

does anyone have any ideas.

Someone at my work says it can only be brute forced, but I don't believe this!

Are any of you smarter..


  • $\begingroup$ (Put on hold because we have a rule here that puzzles not created by the poster must have full attribution -- i.e., say where they came from, so that the actual creator gets the credit they deserve. Unfortunately this produces a message saying the question is "off-topic", which of course it isn't really.) $\endgroup$
    – Gareth McCaughan
    Dec 6, 2019 at 14:09
  • $\begingroup$ Also, it looks to me as if this system of equations doesn't have a unique solution, unless we're supposed to make some assumptions based on the actual colours (e.g., that purple = red + blue). That doesn't seem likely, and in any case if we make all such assumptions that seem plausible the resulting system is inconsistent. $\endgroup$
    – Gareth McCaughan
    Dec 6, 2019 at 15:44

1 Answer 1


I believe

there is no unique solution.

Note that

there are 5 different variables, but only 4 equations, since the 1st and 3rd equations are the same, and the 2nd and 5th equations are the same.

  • 3
    $\begingroup$ A simple RREF of the system demonstrates that any color can only be expressed in terms of another. $\endgroup$ Dec 6, 2019 at 14:10
  • $\begingroup$ If you rotate the lower line (and you see 6 instead of 9), there will be a unique solution for yellow, which is 5...Also, the values range from 1 to 5 (just like the number of the colored equations (two of them being redundant). Maybe the deliberate use of complementary colors ("opposite on the color wheel") bears the message: mirror the lower equation, and that's why. A second reason: nobody told us from what perspective we have to look at an "equation of colors", the whole thing can be upside down. $\endgroup$
    – user63710
    Dec 6, 2019 at 18:35

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