2004 AMC 10A Problem 16

Problem 16 of 25IntermediateCounting & Probability

The

5 \times 5

grid shown contains a collection of squares with sizes from

1 \times 1

5 \times 5.

How many of these squares contain the shaded center square?

Show solution

Solution

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.