2001 AMC 10 Problem 11

Problem 11 of 25IntermediateAlgebra

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

Show solution

Solution

The

n

th ring is the border of a

(2n+1)\times(2n+1)

square surrounding a

(2n-1)\times(2n-1)

square, so it contains

(2n+1)^2-(2n-1)^2=8n

unit squares. For

n=100,

that is

800.

Thus, the correct answer is C.