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This puzzle was part of a competition at my school, over two weeks ago. The school never disclosed the answer, so I'd like to check that I answered it correctly.

What number does each color in the image represent?

enter image description here

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  • $\begingroup$ Editing a question to crop out the context is not proper attribution. $\endgroup$
    – Deusovi
    Apr 26 '20 at 16:54
  • $\begingroup$ @Deusovi MissNature is new to SE, but has done this before. $\endgroup$
    – Galen
    Apr 26 '20 at 17:05
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    $\begingroup$ Questions from other sources must be properly attributed, with full credit given to the question's creators (and a link directly to the source if it's online). $\endgroup$
    – Deusovi
    Apr 26 '20 at 18:03
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    $\begingroup$ it's over 2 weeks ago but they never disclose the answer so i would lile to make sure i answerd it correctly 158 $\endgroup$
    – MissNature
    Apr 26 '20 at 22:07
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    $\begingroup$ I've edited that information into the question and voted to re-open. $\endgroup$
    – F1Krazy
    Apr 27 '20 at 8:28
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Let black be $x$.

The sum of the right-most column is $3x$, which produces a number ending with $x$. The only values of $x$ for which this can happen are 0 and 5.

If we exclude $x=0$ so that the colours are distinct digits, the sum at the bottom is 555.

Dividing by 3 gives you each row:

185

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1
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Because

Let $B$ be the digit represented by the black circle. The main image tells us that $B+B+B=B\pmod{10}$

so

$2B\equiv 0\pmod {10}$, and therefore $B=0$ or $B=5$.

Then:

because all the digits are different, $B=5$ as $B=0$ would mean everything is zero

and as

the three addends are the same, and $\frac{555}{3}=185$, we have:
white is $1$, orange is $8$ and black is $5$.

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