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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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30

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

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4 squares in a 2 by 2 grid 9 squares in a 3 by 3 grid 16 squares in a 4 by 4 grid 25 squares in a 5 by 5 grid 36 squares in a 6 by 6 grid 49 squares in a 7by 7 grid 64 squares in a 8 by 8 grid 81 squares in a 9 by 9 grid 100 squares in a 10 by 10 grid

12 squares.

30

22

There are 4 squares in a 2 x 2 grid.

20

30 squares within a 1 unit grid. 30 squares in all: 4*4 square: 1 3*3 squares: 4 2*2 squares: 9 1*1 squares: 16

4X4

2 x 2 = 4 squares

1+4+9 = 14 squares.

4 x 6 = 24

4 x 4 = 16For any grid n by n, the number of squares is equal to n2 (or n x n)