A classic problem in the study of patterns is the "border problem." A landscaper w...

A classic problem in the study of patterns is the "border problem." A landscaper wants to construct a square patio with light and dark bricks. The figure shows a 3-by-3, a 4-by-4, and a 5-by-5 patio.

a. How many dark bricks does a 6-by-6 patio require?

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b. How many dark bricks does a 13-by-13 patio require?

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c. Find a formula for the number of dark bricks needed for an n-by-n patio.

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d. When does a patio have more light bricks than dark bricks?