All Sizes

How many squares of all sizes are there in a 5 by 5 grid of small squares?

The largest sqare is the one on the outside. The smallest are the 25 making up the grid. I need the total number using all the sizes of squares in the box. Thank you!

You need a way to count without worrying about repetition.
First count all single squares, by counting the centres of the squares. You already said its 5x5.
Next count all 2x2 sqaures. Consider the possible centres of these squares. They can only lie on interior line crossings, of which there are 4x4=16.
For 3x3 squares, you get a 3x3 grid of possible centres, and so on. Cleary there is only one 5x5.

25+16+9+4+1.

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