Problem:
Chubby makes nonstandard checkerboards that have squares on each side. The checkerboards have a black square in every corner and alternate red and black squares along every row and column. How many black squares are there on such a checkerboard?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Separate the modified checkerboard into two parts: the first columns and the last column. The larger section consists of rows, each containing black squares. The last column contains black squares. Thus the total number of black squares is .
There are rows that have black squares and rows that have black squares, so the total number of black squares is .
The problems on this page are the property of the MAA's American Mathematics Competitions