Question

How many squares are there on a checkerboard?
(The answer is not 64.)

Answer 1

1^2 +2^2 +3^2+.... + 8^2= 8*9*17/6=204

Answer 2

@directrix, u know the answer?

Answer 3

(n(n+1)(2n+1))/6 , let n = 8

Answer 4

@Arnabo09 Why do you ask?

Answer 5

then tell me if its correct or not.. i guess u know the answer

Answer 6

I would like to get input from everyone who wants to reply. By then, I will have finished counting on my checkerboard. :)

Answer 7

what i also have found is that a similar approach works for an (albeit imaginary) 3D "chess cube"

the sum of the cubes: (n(n+1)/2)^2

Answer 8

http://answers.yahoo.com/question/index?qid=20060904195928AAf5IgY

Answer 9

oh..
ok..
there will be 8 squares in a row if its length is 1 unit
7 squares in a row if its length is 2 unit..


1 square in a row if its length is 8 unit..
so, total: 1^2+2^2+3^2+..+8^2

Answer 10

what happens if we had a chessboard which isnt square? instead of NxN , we had NxM ?

Answer 11

well, i guess if chessboard is mentioned, it is assumed its 8x8

Answer 12

overlaping or not?

Answer 13

well the problem is solved, i was just suggesting an extension to it

Answer 14

if overlaping:
1+2*2+3*3+4*4+5*5+6*6+7*7+8*8

Answer 15

then the numbers shouldnt be squared..
say, if its 8x6
1 unit length: 8*6
2 unit length:7*5


6 unit length: 3*1..
add these up, @eigen..

Answer 16

if they are alowed to overlap each other, my answer is correct

Answer 17

if you whant i explain....

Answer 18

if not overlaping, you are right

Answer 19

204.
There are 8 different sizes of
squares, ranging from 1 × 1 to 8 × 8.
Only 1 square is 8 × 8, but 4 squares are
7 × 7 and 9 squares are 6 × 6; this pattern
continues through to 64 1 × 1 squares.

Answer 20

I think it is 1 + 4+9+16+25+36+49 +64 ..

Answer 21

Oh fail, I'm too late :S