How many squares are on a chess board?

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ESP-918

Do you know? 

jitterbugflapping
64 8 files x 8 columns
ESP-918
jitterbugflapping wrote:
64 8 files x 8 columns

Incorrect 

Nickchess11322

65!

Nickchess11322

wait no

GroggyNoggin

64 until after the area 51 raid.

DrSpudnik

66: Don't forget the two squares playing the game.

Kjasmine008

65. The shape of the chess board included.

pineapple-on-pizza

There are:

- 8 * 8 = 64 1x1 squares

- 7 * 7 = 49 2x2 squares

- 6 * 6 = 36 3x3 squares

.....

- 1 * 1 = 1 8x8 squares

 

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

BattleCat3

correct

 

DrSpudnik

...and the two squares playing the game.

ESP-918
gjgd wrote:

There are:

- 8 * 8 = 64 1x1 squares

- 7 * 7 = 49 2x2 squares

- 6 * 6 = 36 3x3 squares

.....

- 1 * 1 = 1 8x8 squares

 

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

Did you figure this yourself or looked it up somewhere? 

cellomaster8
It’s simple counting
knightscape007

Now how many cubes are there in a 3D chess board?

DrSpudnik

It boggles the mind.

lindarbj
gjgd wrote:

There are:

- 8 * 8 = 64 1x1 squares

- 7 * 7 = 49 2x2 squares

- 6 * 6 = 36 3x3 squares

.....

- 1 * 1 = 1 8x8 squares

 

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

i dont get it

DrSpudnik

if you take a1, b1, a2, b2 that's another square...and so on

lindarbj
DrSpudnik wrote:

if you take a1, b1, a2, b2 that's another square...and so on

ok,got it. tyhappy.png though those are not squares so it has to be a1a2b1b2 for a square

bartnic1
knightscape077 wrote:

Now how many cubes are there in a 3D chess board?

Seems like its an easy generalization.

8x8x8 + 7x7x7 + 6x6x6 + ... + 1x1x1

Though it's maybe a better question as to how chess would even be played on a 3D board; what we're really envisioning is a 3D cube with a bunch of sub-cubes.

Another interesting question to ask is how many rectangles exist on a chess board? If you like this stuff, then math might be the field for you! happy.png

bartnic1
DrSpudnik wrote:

...and the two squares playing the game.

I like that joke lol. Its "cute"