How Many Squares Are On A Chess Board: Is It 64 or Not?

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How many squares are on a chess board? This article explores that question.

Chess is a game played by two players on a checkered board. Chess is a strategic and tactical game representing “a war scenario” where two kingdoms fight each other in an attempt to triumph over the other. In this game, we say that a particular side has won when the opponent’s king has been “checkmated”.

A chess board containing 16 white pieces and 16 black pieces
A 2D version of a chess game

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 Chess Board Have? 

Didn’t we just discuss that earlier? It’s easy to jump to 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.

Why Is The Total Number Of Squares On A Chess Board Greater Than 64 And Equal To 204?

Let’s take a look at things from a mathematical perspective. You are not just looking at the individual square units but the “square within the squares”

To learn more, look at the diagram below.

The Chess Board

We take the following simple process to decipher the answer.

Step 1 = 1 × 1 squares (refers to the dimension) – 8 squares across the width and 8 squares along the length = 8 × 8 = 64 squares 

Step 2 = 2 × 2 squares (refers to the dimension) – with the size of the square increasing by 1 square the number of squares across the width will be down to 7 and the ones along the length will also be down to 7. So, there are 7 × 7 = 49 (2 × 2) squares.

Step 3 = 3 × 3 squares (refers to the dimension) – 6 squares across the width and 6 along the length = 6 × 6 = 36 (3 × 3) squares.

Step 4 = 4 × 4 squares (refers to the dimension) – 5 squares across the width and 5 along the length = 5 × 5 = 25 (4 × 4) squares.

Step 5 = 5 × 5 squares (refers to the dimension) – 4 squares across the width and 4 along the length = 4 × 4 = 16 (5 × 5) squares.

Step 6 = 6 × 6 squares  (refers to the dimension) – 3 squares across the width and 3 along the length = 3 × 3 = 9 (6 × 6) squares.

Step 7 = 7 × 7 squares  (refers to the dimension) – 2 squares across the width and 2 along the length = 2 × 2 = 4 (7 × 7) squares.

Step 8 = 8 × 8 squares  (refers to the dimension) – 1 square across the width and 1 along the length = 1 × 1 = 1 (8 × 8) square.

Therefore, adding up all these squares, we have  64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares all on a chessboard! 

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