imc

Question

Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains 8 unit squares. The second ring contains 16 unit squares. If we continue this process, the number of unit squares in the 100^th ring is FIGURE

Accepted Answer

We can partition the n^th ring into 4 rectangles: two containing 2n+1 unit squares and two containing 2n-1 unit squares. There are 2(2n+1)+2(2n-1)=4n+2+4n-2=8n unit squares in the n^th ring. Thus, the 100^th ring has 8 100 = 800 unit squares.