Question

Square ACEG is drawn at the right. Points

B, D, F, and Hare the midpoints of the sides
of the square. What is the total number of
squares of all sizes which can be traced using
only the line segments shown?

Answer 1

We can approach this problem systematically by counting the number of squares of each size. Let's start with the smallest squares and work our way up to the largest.

1x1 squares: There are 16 of these squares, each formed by the intersection of two adjacent line segments.

2x2 squares: There are 9 of these squares, each formed by four adjacent 1x1 squares.

3x3 squares: There are 4 of these squares, each formed by nine adjacent 1x1 squares.

4x4 squares: There is only 1 of these square, which is the square ACEG itself.

Therefore, the total number of squares of all sizes that can be traced using only the line segments shown is 16 + 9 + 4 + 1 = 30

Explanation:

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