May 2014
Problem of the Month

Checkerboard Problem

A standard checkerboard with 8 blocks to a side contains 204 squares of various sizes.

How many of those 204 squares contain an equal number of red blocks and black blocks?

Solution to the Problem:

The answer is 84 squares.

You must determine how many of the squares have an area that contains an even number of blocks.

Dimensions of Square	Number of Squares with those dimensions
1 x 1	64
2 x 2	49
3 x 3	36
4 x 4	25
5 x 5	16
6 x 6	9
7 x 7	4
8 x 8	1

So, add up the number of squares with even dimensions:
49 + 25 + 9 + 1 = 84 squares.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Chase L. Smith	Mountain View High School, Mountain View, Wyoming
3. John Campbell	Carlisle, Pennsylvania
4. Carrie Cotter	York Community High School, Elmhurst, IL
5. Marley Newton	Mountain View High School, Mountain View, Wyoming
6. Hannah Bugas	Mountain View High School, Mountain View, Wyoming
7. Philip Regalado	John Paul II Catholic High School, Tallahassee, Florida
8, Adrianna Quintero	John Paul II Catholic High School, Tallahassee, Florida
9. Sara Alda Justicia	Mountain View High School, Mountain View, Wyoming
10. Levi Hanney	Mountain View High School, Mountain View, Wyoming
11. Alex Houskeeper	Mountain View High School, Mountain View, Wyoming
12, Austin Houskeeper	Mountain View High School, Mountain View, Wyoming
13.Bailey Lupher	Mountain View High School, Mountain View, Wyoming
14. Samantha Brailsford	Mountain View High School, Mountain View, Wyoming
15. Dalton Hereford	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher