2001 AMC 10 Problem 11

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

396

404

800

10{,}000

10{,}404

The

n

th ring is a

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

square with the

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

square removed

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

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.

Problem 11 in other years