How Many Squares on a Chess Board?

I count 204 squares.

How did I arrive at that number?

• 64 - There are 64 grids of 1 x 1
• 49 - There are 49 grids of 2 x 2
• 36 - There are 36 grids of 3 x 3
• 25 - There are 25 grids of 4 x 4
• 16 - There are 16 grids of 5 x 5
• 9 - There are 9 grids of 6 x 6
• 4 - There are 4 grids of 7 x 7
• 1 - And of course the 1 square that makes up the whole thing.

Total: 204 squares.

As a programming function (in PHP), it's pretty simple:

$x = 8; //Grid size assumes square, not rectangle

function squares($x){

$total = 0; //Initialize total

while($x > 0){

$total += ($x * $x); //Current total + calculated value of $x $x

$x--; //Subtract 1 from current value of $x

}

return $total;

}

echo squares($x);

If you wanted to be even more literal minded, you could make argument for 189 squares on a physical board if you counted the bottom of the board and that it was blank. For a digital board, you could get really crazy and count the number of pixels and then apply the same reasoning used on that grid and add 188 to it.

This is one of those math problems in books and in S.A.T. tests that have to basis in reality.

But that's another story.

I brought this up on Math Forum dot com or something like that and got banned because math professors like to live in their artificial worlds.

Numbers are meaningless to me if they have no basis in reality. I'm a programmer so the numbers I'm generally dealing with represent real things, generally stored in a database or displayed to a user.

I realize that there's a place for theoretical math, I just nave no use for it myself.

What's the point of a response like that other than to clutter up a discussion and pollute notifications? Go away.

I might actually answer your question if you weren't rude.

No I wasn't. I asked a legitimate question.