A quilter sews large squares made of small gray and white squares, as shown. The design depends on the size of the large square. The diagram shows the sequence of designs.

Question

The quilter wants to make large squares that each have a total of 64 small squares. How many white small squares are needed for each large square the quilter makes?

44

36

50

32

Answer 1

To determine how many white small squares are needed for a large square containing a total of 64 small squares, we first recognize that a large square with 64 small squares must be \(8 \times 8\) since \(8 \times 8 = 64\).

Next, let's consider the pattern of the colors in the design. Designs that depend on alternating colors are often structured in a checkerboard or similar format. A common design would include half of the small squares in one color and half in another color.

In an \(8 \times 8\) square:

• There are a total of 64 small squares.
• If the design follows a checkerboard pattern, you would have:
  • 32 small squares of one color (e.g., gray)
  • 32 small squares of another color (e.g., white)

Therefore, in the case of an 8x8 square made following the typical checkerboard pattern:

• The number of white small squares = 32.

So, for a large square containing 64 small squares, the quilter would need 32 white small squares.