What is the total number of squares on chessboard?

Answer is not as simple as it seems at first site.

Nobody?? I thought there are few maths students on this site! And moreover.. Answer is not 64!

17   (I'm pretty sure of it)

1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 = 204.

I also got 204.

Edit: I accidentally typed 2044 at first.

Nilotpal and Franksmith.. Can you elaborate your answers for other user?

85

42. The answer is most definitely 42.

it is simple! im 13 and I can get it...

8 squared for the initial 64 squares that we play chess on, then 7 sqaured for the 2 by 2s and so on. the answer is 204 sqaures

Age Range: 7 to 11

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The number of rectangles in a chessboard is actually equal to the sum of the cubes of the consecutive numbers from one to eight.

Hence,

8^3 + 7^3 + 6^3 + 5^3 + 4^3 + 3^3 + 2^3 + 1^3 = 1296.

As easy as the number of squares.

ok I get it, but it is not as simple as the squares because cubing makes you think of.. well a cube... here you are taking into account all of the other varients of a rectangle (squares included) so it is not imidietly obviouse that you should cube it.

9 quintillian rice

There are generally at least two squares on any board - the one who's playing white and the one whose's playing black.

@cjt33: There is a much simpler way to do this. Just follow this formula:

Number of rectangles (nxn board) = [n(n+1)/2]^2 = [8*(9)/2]^2 = 36^2 =1296.

I think, you will now agree that this is very easy! Lol!

Just in case you don't want to use the formula then just add the numbers from 1 to 8 and square the sum.

 (1 + 2 + 3 + 4 + 5 + 6 +7 + 8 )^2 = 1296

Now, you are not thinking of a cube.

OK.  How many 8x8 squares are there? 1 (=1 squared).

How many 7x7 squares are there? 4 (2 squared).  If you try to shift a 7x7 square around the chessboard, and focus on one corner (like the bottom left corner), it can only be at a1, a2, b1, b2.

How many 6x6 squares are there?  Now the corner can be anywhere in a 3x3 box (a1,2,3; b1,2,3; c1,2,3).  The answer is 9 (3 squared).

And so on up to 1x1 squares, which can be in 8 squared possible locations.

teny, those seem to get the answer and I understand the formula, but why would you do (1+2+3+4+5+6+7+8)^2? It kind of seems like finding a random way to do the problem that kind of coincidentally works...

if I am wrong then please correct me