How Many Squares on a Chessboard?

Seven.

• Square-Size 1x1 --> 64
• Square-Size 2x2 --> 49
• Square-Size 3x3 --> 36
• Square-Size 4x4 --> 25
• Square-Size 5x5 --> 16
• Square-Size 6x6 --> 9
• Square-Size 7x7 --> 4
• Square-Size 8x8 --> 1

64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204

Not every rectangle is a square.

I want to change my answer.

I'm going to say... nine.

Sum (8x8 + 7x7 + 6x6 + 5x5 +4x4 +3x3 + 2x2 +1x1)

This way it can be calculated for any size.

If you want to calculate for any size, you need to use the letter n because that's what math people do.

So for an nxn board the answer is

nxn nxn nxn nxn . . . nxn

qed

make it as simple as possible here

and your answer for nxn is wrong

nxn=n

easy!

n∈

 Yeah, the simplification of squares and rectangles are really cool.

For example the number of rectangles is 8^3 + 7^3 + 6^3 + . . . + 1^3

Which I'm not sure has an easy way to visualize.

But counting the squares does have an easy way to visualize.

There is one 8x8 square, there are four 7x7 squares, nine 6x6 squares . . . 64 1x1 squares.

Then add a couple for the 2 squares playing the game.

204 to be precise.

iballisticsquid123 wrote:

basically 8x8+7x7+6x6+5x5+4x4+3x3+2x2+1x1

Dammit!!! I worked it out and then saw your post.

I can... there are three rooms. One is filled with important papers. Another is filed with money. The last room is filled with jewelry. One day, all of the rooms set on fire. Which room did the policeman put out first?

yeah

good job guys want more riddles?

No, the real question is:

How many triangles are there on a chess board?