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Chess Math Problem Problem

Chess Math Problem Problem

Posers and Puzzles

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How many different spuares are there on a 8x8 checherboard?

You can find more than 64 I'll give you that much.

Explain your answer and how you did it.

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Originally posted by Lord Burn
How many different spuares are there on a 8x8 checherboard?

You can find more than 64 I'll give you that much.

Explain your answer and how you did it.
1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2
= 204
[ = 8*(2*8+1)*(8+1)/6 from the formula for the sum of consecutive squares]

We get this because there is one way of placing an 8*8 square on the chessboard, four ways of placing a 7*7 square etc.

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Originally posted by Lord Burn
How many different spuares are there on a 8x8 checherboard?

You can find more than 64 I'll give you that much.

Explain your answer and how you did it.
Here's another one

You have 3d chessboard of size N^3

How many different vertical and horzontal squares are there on this chessboard?

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Originally posted by Lord Burn
How many different spuares are there on a 8x8 checherboard?

You can find more than 64 I'll give you that much.

Explain your answer and how you did it.
2, a white one and a black one.

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Originally posted by TheMaster37
2, a white one and a black one.
I guess that's Dutch Logic...😀

Olav

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Originally posted by iamatiger
Here's another one

You have 3d chessboard of size N^3

How many different vertical and horzontal squares are there on this chessboard?
Well, in each of the cubes you've got an uncountable infinity of squares.