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The first question that arises when we begin to draw squares around the numbers is: How many unique squares can be drawn within the grid It is dependent upon the length of the sides of the square. A table is given below:

Using the same grid, we will calculate the difference in the product of the corners.

## Introduction

This is true for a 2 x 2 square and all other sizes. However, the difference in the product of the corners is dependent upon the size of the square. As the size of the square gets larger, the difference in the product of the corners also increases.

But is there an algebraic relationship between the size of the square and the difference of the product of the corners Can we calculate the difference by knowing the size of the square Table 10 lists the results from the previous investigations.

As we have seen, no matter what size square is used, we can use algebra to calculate the number of possible squares and the difference in the product of their corners. This applies to all possible combinations placed on the grid.

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