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Squares on a Chessboard Challenge

Hey guys! :wavey:

I have an interesting puzzle/challenge here for you guys! There is no required knowledge for this, so anyone can have a go. :biggrin:



This is a standard 8x8 chessboard. If I asked you how many squares were on there, you may count up all of the black and white small squares and end up with 64.

However you need to consider that other squares can be formed using the smaller squares, such as a 2x2 square as demonstrated below:

square.png

The questions are:
How many squares on a 8x8 chessboard?
How many squares on are on a nxn chessboard?
Is there a way to work out how many rectangles there are?

Please post your answers in the following format:

[noparse]

Spoiler

[/noparse]
(edited 7 years ago)
:bump:
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Avatar for sputum
sputum
9

Spoiler

maybe an answer to the 3rd part of the question, although i dont have much confidence in it :dontknow:

Spoiler

Original post by DylanJ42
So number of rectangles on 8x8 is number of shapes - number of squaresUm, a square is a rectangle, so there's no reason to exclude the squares...
Original post by DFranklin
Um, a square is a rectangle, so there's no reason to exclude the squares...


oh i didnt know, whoops

I guess ignore the "minus squares" part then

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