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 |