Problem:
A checkerboard consists of one-inch squares. A square card, inches on a side, is placed on the board so that it covers part or all of the area of each of squares. The maximum possible value of is
Answer Choices:
A. or
B. or
C. or
D. or
E. or more
Solution:
Using the Pythagorean Theorem, the length of the diagonal of the card is . This is longer than , the length of two adjacent squares. The figure shows squares being touched.
Query. Is the maximum number of squares that can be touched?
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions