how many squares are in a 8x8 checkerboard?

Question

and i already know there are waaay more than 64

Answer 1

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

sum(i=1 to 8; i^2) = 204

if you are allowing 1x1's

Answer 2

Answer: 204 squares

Consider that each side of the checkerboard is 8units.

Then there are 8*8= 64 1unit*1unit squares
There are 7*7 = 49 2unit*2unit squares
6*6 = 36 3unit*3unit squares
5*5 = 25 4unit*4unit squares
4*4 = 16 5unit*5unit squares
3*3 = 9 6unit*6unit squares
2*2 = 4 7unit*7unit squares
1*1 = 1 8unit*8unit squares

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

Or you can use the formula

1^2 + 2^2 + - - - + n^2= n(n+1)(2n+1) / 6

here n=8,

so answer= (8 * 9 * 17) / 6 =204

Answer 3

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There are 64 playing squares on a checkerboard. Checkerboards have 8 rows of 8 squares each, in alternating colors, usually black and red. Geometrically speaking, however, there are actually 204 squares on an eight-by-eight checkerboard! 64 1x1 squares 49 2x2 squares 36 3x3 squares 25 4x4 squares 16 5x5 squares 9 6x6 squares 4 7x7 squares 1 8x8 square

Answer 4

There are quite a few! This is an interesting problem. Let's tackle
the one about the squares first. There is only ONE 8x8 square. There
are FOUR 7x7 squares. There are NINE 6x6 squares, and so on. You can
see this by taking a square (say 6 by 6) and seeing how many squares
you can move it horizontally and how many vertically and multiplying
these two numbers together). If you see the pattern above, the answer
to the question as to how many squares there are is

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

The "equation" you want is N = (9-s)^2 where N is the number of
squares of side s. That is, for a square of N sides, the total number
of squares = 1^2 + 2^2 + 3^2 + ... + N^2.]

Answer 5

Checkerboard Squares

Answer 6

Squares On Checkerboard

Answer 7

This Site Might Help You.

RE:
how many squares are in a 8x8 checkerboard?
and i already know there are waaay more than 64

Answer 8

Yipe !!! She did not tell us the size of the squares she wanted us to count. My gosh this must be a trick question. Could it be that she wants the number of all possible squares within a checkerboard pattern of the shape 8 X 8, where there are nine horizontal lines and nine vertical lines, all equaldistant and suitable for sides/top-bottoms of our squares? Yes, yes, yes...

She told us there were more than 64.

Answer 9

come on people think about the bigger picture...im not going to figure this whole thing out but you have to realise that, yes there are 64 small squares and then 4 of those make a larger square and16 make an even larger untill eventually the checkerboard itself makes the largest square. simple, but i dont feel like counting, someone else can do that...

Answer 10

the answer is in what you said

8 x 8 = 8 times 8 = the number 8 added 8 times, which is:

64!

Please though, elaborate on why you feel there are more than 64.


You know, if some one asks me how many individual squares there are, then I answer. No one said how many possible square combinations you could make out of a 8x8 checkerboard... gosh.