1009.21 – Squares on a Checkerboard


How many squares are on or inside a checkerboard? (Hint: More than 64.)


Solution

Here is a tally of the squares.

1×1:642×2:493×3:364×4:255×5:166×6:97×7:48×8:1\begin{aligned}1 \times 1 &: 64 \\2 \times 2 &: 49 \\3 \times 3 &: 36 \\4 \times 4 &: 25 \\5 \times 5 &: 16 \\6 \times 6 &: 9 \\7 \times 7 &: 4 \\8 \times 8 &: 1 \end{aligned}

The total number is 204. Interesting numbers, eh?