Four ( $4 \times 7$) rectangles are removed from the corners of a square having side length ($8n + 1$), as shown in the Figure. Determine the largest integer $n $ for which the perimeter of Figure is less than $1000$.
The removal of the rectangles does not affect the perimeter.......the firgure has exactly the same perimeter as that of the square
So
4 (8n + 1) < 1000
32n + 4 < 1000
32n < 996
n < 996 / 32
n < 31 + 1/8
So n = 31
