2004 AMC 10A Problem 16

Question

The

5 \times 5

grid shown contains a collection of squares with sizes from

1 \times 1

to

5 \times 5.

How many of these squares contain the shaded center square?

12

15

17

19

20

Every

3\times3,

4\times4,

and

5\times5

square contains the center

Then count how many

2\times2

and

1\times1

squares cover the center cell

Every

5\times5,

4\times4,

and

3\times3

square contains the center cell, and there are

1^2 + 2^2 + 3^2 = 14

of them.

Among the smaller squares,

4

of the

2\times2

squares and

1

of the

1\times1

squares cover the center, giving

14 + 4 + 1 = 19.

Thus, the correct answer is D.

Problem 16 in other years