# Complete the pattern

I have been creating puzzles to promote our school's Facebook page, but in a week no-one could yet answer this one:

Complete the pattern:

It is:

C

because:

Let white=0, grey=1, black=2. Adding the first two squares from either rows or columns and subtract 3 if the answer is greater than 2 gives the third square in the row/column.

C

Because:

Black + black = gray.
Gray + gray = black.
Color + white = color.

• What about Black + Gray? – ibrahim mahrir Jul 16 '18 at 19:09
• @ibrahimmahrir It looks like Danne used the term "color" to mean either black or grey. That makes sense when also considering how other answers assign the value of $0$ to white, as $x + 0 = x$. – maxathousand Jul 16 '18 at 21:03
• Don't forget: White $+$ White $=$ White. – Feeds Jul 16 '18 at 21:59
• @maxathousand But that when "color" is added to white. I'm asking about Black + Gray. – ibrahim mahrir Jul 16 '18 at 22:12
• @ibrahimmahrir oh wow, hahha totally misread that. You’re right – maxathousand Jul 17 '18 at 0:38

Assign black, grey, and white the values, and 0 respectively (Black would be 2, grey 1, and white 0). Now the top-left square would look like this: $$\begin{bmatrix}2 & 1 & 0\\1 & 2 & 1 \\0 & 1 & 2 \end{bmatrix}$$ And the middle-left like this: $$\begin{bmatrix}0 & 0 & 0\\1 & 1 & 1 \\2 & 2 & 2 \end{bmatrix}$$ Adding them together would result in a square looking like this: $$\begin{bmatrix}2 & 1 & 0\\2 & 3 & 2 \\2 & 3 & 4 \end{bmatrix}$$ Which has values greater than 2, so we use a modulo function (which gives the remainder of a division) to subtract three from all values greater than 2, gives a box with the following values: $$\begin{bmatrix}2 & 1 & 0\\2 & 0 & 2 \\2 & 0 & 1 \end{bmatrix}$$ Which is the bottom-left matrix. Doing this procedure to the right column gives you a matrix with the values of C.
• Hello! Welcome to the Puzzling Stack Exchange (PSE). Congratulations on your very first answer, here, and it is a great one too — it is thorough; well-explained; and easy to understand. However, since you are new, I advise that you visit the Help Center and, since you have not asked a question as of yet, I highly suggest you go here and here to look at info about questions. Otherwise, keep puzzling! $$\stackrel{\bullet\,\bullet}{\smile}$$ – Feeds Jul 16 '18 at 22:04