# What number does each color in the image represent?

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?

• Editing a question to crop out the context is not proper attribution.
– Deusovi
Apr 26 '20 at 16:54
• @Deusovi MissNature is new to SE, but has done this before. Apr 26 '20 at 17:05
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– Deusovi
Apr 26 '20 at 18:03
• it's over 2 weeks ago but they never disclose the answer so i would lile to make sure i answerd it correctly 158 Apr 26 '20 at 22:07
• I've edited that information into the question and voted to re-open. Apr 27 '20 at 8:28

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

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 $$5$$.