Problem:
A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is , how many tiles cover the floor?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the total number of tiles in the two diagonals is , there are tiles in each diagonal (with one tile appearing in both diagonals). The number of tiles on a diagonal is equal to the number of tiles on a side. Therefore, the square floor is covered by square tiles.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions