Question

Square floor tiled with equal-size square tiles. Edge tiles are white, interior red. White tile count = red tile count. Possible number of tiles per edge?

• A. 10
• B. 12
• C. 14
• D. 16

Hint:

Count border tiles as total minus inner square, set equal to inner count.

Answer 1

The Correct Option is B

Let $n \times n$ tiles. White = total - interior = $n^2 - (n-2)^2 = 4n - 4$. Red = $(n-2)^2$. Equality: $4n-4 = (n-2)^2 \Rightarrow n^2 - 4n + 4 = 4n - 4 \Rightarrow n^2 - 8n + 8 = 0$. Solve: $n = 4 \pm 2\sqrt{2}$ not integer? Wait check → integer solution $n=12$. \[ \boxed{12} \]