Question

The First 4 stages of a certain fractal are shown. In each stage after the first, each square is divided into 4 squares, and then the bottom right square is removed. If the pattern continues, how many shaded square units will stage 5 contain?

• A. 243
• B. 54
• C. 81
• D. 27

Answer 1

The correct option is C 81

Stage 1: 1 Square
Stage 2: The square is divided into four parts and bottom part is being removed. Hence total squares remaining $=4-1=3$

Stage 3: All the three squares are divided into four parts and bottom part is removed.
So, the remaining squares $=3\times 4-3=9$
Stage 4: All the nine squares are divided into four parts and bottom part is removed.
So, the total no. of remaining squares $=9\times 4-9=27$
Stage 5: All the 27 squares are being divided into four parts and bottom part of all the squares is removed.

Thus, the no. of squares remaining $=27\times 4-27=81$.

Hence, option C is correct.