How Many Squares Are On A Chessboard?
This question could be quite tricky in chess trivials. The obvious answer is 64 since there are 32 light squares and 32 dark squares on a chessboard. But you forget the square that contains all the 64 squares, and this makes the total number of squares equal to 65.
Interesting, right? Let’s look at other possible ways to calculate the number of squares on a chessboard.
Another perspective you can take is looking at the squares without their colours and how they all come together to form a chessboard.
Although this perspective seems quite simple, the truth is that it requires a systematic approach to attain the correct answer.
First, you have to find out how many possible squares you can get from the 64 squares on a chessboard. You do this by creating a bigger unit of squares with each square on the board.
|Unit||Horizontal number of square||Vertical number of square||Total Number of square|
You’ve probably seen a pattern by now. As we progressively make the target square smaller by one unit, we can find this a perfect square number of times.
There are 2×2 starting positions a (7×7) square can start from, and there are 3×3 starting positions a (6×6) square can start from, there are 4×4 starting positions a (5×5) square can start from e.t.c
This way, you’ll get 203 squares from the initial 64. Adding the 1 square that contains all 64 squares gives you 204 squares on a chessboard.