Are all your squares the same size? (I can see some that are bigger than others...)How many different sizes of square are there?How many squares are there of each size?Would it help to start by counting the squares on a smaller board first?Is there a quick way to work out how many squares there would be on a 10x10 board? Or 100x100? Or...?What about a rectangular chessboard?

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Answer


There are 64 blocks which are all the same size. All you had to do was 8 times 8 which equals 64 because it is aboard that is 8 by 8.

You are watching: How many squares in a chess board


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I can see what you mean, but...


I see the 64 squares you mean. I can see some other squares too, of different sizes. Can you find them?


invernessgangshow.net / Chessboard squares


I also see there are 64 squares ("cause 8 x 8 is 64). However, all the squares have the same size. Why? Well, I measured it with a ruler and they all have the same size. Sometimes, our eyes see illusions instead of the reality. Check it.


Mathematics / Chessboard


Luisa saw that there were bigger squares because the question is "How many squares are there?" But it doesn't clarify what type of squares, so there are bigger and smaller squares, meaning, there are more than 64 squares. The bigger squares are composed by smaller squares. So a big square would have 4 mini small squares. (Bigger ones could have more :) )

PS: If a question is posted by Cambridge, well we can guess it won't be some very easy questions. :)


Chessboard Challenge


The answer is 204 squares, because you have to add all the square numbers from 64 down.


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That's an interesting answer


That"s an interesting answer - can you explain why you have to add square numbers?What about for different sized chessboards?


represent each type of square


represent each type of square as a letter or symbotogether ,and use that as a quick way to work out how many of each type of square.


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Interesting strategy - could


Interesting strategy - could you explain a little more about how you could use it to find the solution?


answer


you can work this out by drawing 8 separate squares, and on each find how many squares of a certain size are there. For 1 by 1 squares there are 8 horizontally and 8 vertically so 64.For 2 by 2 there are 7 horizontally and 7 vertically so 49 . For 3 by 3 there are 6 and 6, and so on and you find that after you have done that for 8 by 8 you can go no more so add them up and find there are 204.


Interesting...


There are actually 64 small squares, but you can make bigger squares, such as 2 times 2 squares


chessboard challenge


we have predicted that there are 101 squares on the chessboard. There are 64 1 by 1 squares,28 2 by 2 squares,4 4 by 4 squares,4 6 by 6 squares,1 8 by 8 square ( the chessboard)


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Have you missed some?


Some people have said there are more than 101 squares. Perhaps you have missed some - I can spot some 3 by 3 squares for example.


answer strategy


The answer is 204.My method: If you take a 1 by 1 square you have one square in it. If you take a 2 by 2 square you have 4 small squares and 12 by 2 square. In a 1 by 1 square the answer is 1 squared, in a 2 by 2 square the answer is 1 squared + 2 squared in a 3 by 3 square the answer is 1 squared + 2 squared + 3 squared, etc. So in an 8 by 8 square the answer is 1 squared + 2 squared+ 3 squared + 4 squared + 5 squared + 6 squared + 7 squared + 8 squared which is equalled to 204.


Chess board challenge


There are 165 squares because there are 64 of the tiniest squares and 101 squares of a different bigger size, combining the tiniest squares into the bigger ones.


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How did you work it out?


I found more than 101 bigger squares. How did you work them out? Perhaps you missed a few.


Total 204 squares


Total 204 squares8×8=17×7=46×6=9......1×1=64Total204


My solution


I came to the conclusion that the answer is 204.

Firstly, I worked out that there were 64 'small squares' on the chess board.

The next size up from the 1x1 would be 2x2 squares.Since there are 8 rows and columns, and there is an 'overlap' of one square for each of these, there are 7 2x2 squares on each row and each column, so there are 49. What I mean by overlap is how many squares longer by length each square is than 1.

For 3x3 squares, there is an overlap of 2, and so there are 8 - 2 squares per row and column, and therefore 6x6 of these, which is 36.

For 4x4 squares, the overlap is 3, so there are 5 per row and column, leaving 25 squares.

This is repeated for all other possible sizes of square up to 8x8 (the whole board)

5x5: 166x6: 97x7: 48x8: 1

64+ 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204.

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Interestingly, the quantities of the squares are square numbers which decrease as the size of the square increases - this makes sense as the larger the square, the less likely there is going to be sufficient space in a given area for it to fit. It also makes sense that the quantities are square numbers as the shapes we are finding are squares - therefore, it is logical that their quantities vary in squares.