SOLUTION: A square checkerboard is made up of 36 alternately colored 1 inch by inch squares. What is the total number of squares that are visible on this checkerboard.(hint: count the 6 by

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A square checkerboard is made up of 36 alternately colored 1 inch by inch squares. What is the total number of squares that are visible on this checkerboard.(hint: count the 6 by       Log On


   

Question 401351: A square checkerboard is made up of 36 alternately colored 1 inch by inch squares. What is the total number of squares that are visible on this checkerboard.(hint: count the 6 by 6 squares, then the 5 by 5 squares, and so on.) How many are visible on a checkerboard that has 64 alternately colored 1 inch by 1 inch squares?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
On the 6x6 checkerboard, there is 1 6x6 square, 4 5x5 squares, 9 4x4 squares, ..., 36 1x1 squares. Therefore the number of total squares is

sum%28k%5E2%2C+k+=+1%2C+6%29+=+6%287%29%2813%29%2F6+=+91 (applying the sum of squares formula)

Likewise, with the 8x8 checkerboard, the total number of squares is

sum%28k%5E2%2C+k+=+1%2C+8%29+=+8%289%29%2817%29%2F6+=+204