How Many Black And White Squares Are On A Chess Board?
Like noted earlier, Chess is played on a checkered board and this board has 64 squares. And it’s easy to notice that this board consists of alternating black and white squares.
Counting these squares will total to 32 Black squares and 32 White squares resulting to 64 Black and White Squares. The chess board is made up of files (1-8) and ranks (a-h). This helps with correct placement of the board as one must be aware that the bottom left of the board has a dark square while the top left has a white square.
So How Many Squares Does A Standard Chessboard Have?
Let’s return to the “how many squares are on the chessboard” question. But we discussed that earlier, right? It’s easy to jump to a conclusion here and come up with 64 squares, but is it actually correct?
Of course, if you’re simply looking at the small squares occupied by the pieces during a game of chess or draughts/checkers, that’s the proper answer.
But what about the larger squares that result from combining these small squares? If you consider each square of various sizes on a chess board instead of the individual square units, you’re gonna be having much more than 64. The total number of squares will be 204.
How Many Squares Are On A Chessboard? Mathematical Breakdown
Another perspective you can look at is the squares without their colors 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.
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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 |
| 1×1 | 8 | 8 | 64 |
| 2×2 | 7 | 7 | 49 |
| 3×3 | 6 | 6 | 36 |
| 4×4 | 5 | 5 | 25 |
| 5×5 | 4 | 4 | 16 |
| 6×6 | 3 | 3 | 9 |
| 7×7 | 2 | 2 | 4 |
| Total | 203 |
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, etc.
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.
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