Problem:
Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains unit squares. The second ring contains unit squares. If we continue this process, the number of unit squares in the ring is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The ring can be partitioned into four rectangles: two containing unit squares and two containing unit squares. So there are
unit squares in the ring. Thus, the ring has unit squares.
The ring can be obtained by removing a square of side from a square of side . So it contains
unit squares.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions