How Many Squares on a Chessboard?

Factor Analysis: for some, it's less: for others, it's more.

Ciao

Mind you, it is a chess board. Chess being optimal, therefore, 0 does not play into the equation!

Ciao

There again, with perfect play the number is callable! Therefore it is not subject to a proposition.

Ciao

i looked it up....204....64+49+36+16+9+4+1=204

We can look at the board as a 9 by 9 square lattice and try to count the number of squares having their vertices on lattice points. With this definition, we also include tilted squares. These squares have the particularity of being inscribed in a bigger non-tilted square with its vertices also on lattice points. The number of squares inscribed in a non tilted square with side length k is k because each lattice point (k+1 of them) on the upper side of the non-tilted square uniquely describes a square except for the first and last points which both describe the initial non-tilted square, so (k+1)-1=k. Hence, the number of tilted squares is the sum k(n-k)^2, (n-k)^2 giving the number of non-tilted squares of side length k, which computes to be 540 for n=9.

ℵ₁

Number of 1x1 squares on a chessboard: 64

Number of 2x2 squares on a chessboard: 49

Number of 3x3 squares on a chessboard: 36

Number of 4x4 squares on a chessboard: 25

Number of 5x5 squares on a chessboard: 16

Number of 6x6 squares on a chessboard: 9

Number of 7x7 squares on a chessboard: 4

Number of 8x8 squares on a chessboard: 1

(Notice the power of 2 pattern.)

Total: 204

But you've only shown eight squares.

306

you should have stuck with this the first time.

How about this without math?

Hypothetical: A sole Black King on a chess board vs White King and a pawn all of the pieces in their starting position. Engine states mate in 49 or something or another, every move the squares are counted again.

Multi-dimensional chessboard squares!

Ciao

Before I clicked on this, I thought this was coming from a noob who doesn't use google

64.64.64 64 64 64

Halahalahala

So, what's the answer?  i said 204 but can anyone provide a definitive answer?

204

Having been here a few years.  You would get page after page after page of people arguing over absolutely anything.

I betcha a post along the lines of: "I danced on the sun last week.  Prove i didn't"  Would get at least 100+ comments.

what about this: you read this wrong or not

Cucumber...see...I can do it too.