1. On a Pascal's triangle template shade the squares containing odd numbers. Using the arithmetic facts odd + odd = even, even + even = even, odd + even = odd, and even + odd = odd, explain why the Sierpinski gasket appears.
Hint: explain why the next-to-the leftmost column and the first subdiagonal (the diagonal immediately below the hypotenuse of the triangle, whose squares all contain 1s) alternate even and odd numbers. Does this suggest a way to approach the general problem?
2. On a Pascal's triangle template shade the squares containing numbers that are not multiples of 3. Use addition mod 3 to explain why a relative of the Sierpinski gasket appears.
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