Question

The diagram represents a $7$ -foot-by- $7$ -foot floor that is tiled with $1$ -square-foot shaded tiles and unshaded tiles. Notice that the corners have unshaded tiles. If a $15$ -foot-by- $15$ -foot floor is to be tiled in the same manner, how many unshaded tiles will be needed?

$49$

$57$

$64$

$96$

$126$

Solution:

In the $7\times7$ example, there are $4$ rows that contain $4$ unshaded tiles, for $4^2=16$ unshaded tiles.

For a $15\times15$ floor with the same pattern, there will be $8$ such rows with $8$ unshaded tiles each.

Thus the number of unshaded tiles is $8^2=64$ .

Thus, C is the correct answer.

2009 AMC 8 Problem 18

Solution:

Problem 18 in Other Years