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How many squares are there in a 4 by 4 grid?

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There are 30 squares in a 4 by 4 grid. Here's how it breaks down.
There are 16 of the 1 x 1 squares.
There are 9 of the 2 x 2 squares.
There are 4 of the 3 x 3 squares.
There is 1 of the 4 x 4 squares.
It's fairly easy to see the individual 1 x 1 squares and count them. Same with the 4 x 4 square, as it's the perimeter of the whole array. With the 2 x 2 squares, start with a 2 x 2 square in, say, the upper left corner and "move" the square one space to the right. Then one more to "complete" the top row. Then move it one square "down" and continue until arriving at the place you started. There will be 9 different "positions" for the 2 x 2 square.
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How many squares and rectangles are there in a 4 by 4 grid?

16 1x1 rectangles + 12 2x1 rectangles + 8 3x1 rectangles + 4 4x1 rectangles + 12 1x2 rectangles + 9 2x2 rectangles + 6 3x2 rectangles + 3 4x2 rectangles + 8 1x3 rectangles + 6

How many squares in a 4 x 4 grid?

16   Answer #2   It is 16 if you just count the 1 x 1 squares but the 16 squares also form a 4x4 square. There are also 2x2 squares and 3x3 squares in the pattern.