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2011 AMC 10A Question 3

AMC10 · 2011 AMC 10A

Question 3

Suppose $[a\ b]$ denotes the average of $a$ and $b,$ and $\{a\ b\ c\}$ denotes the average of $a,$ $b,$ and $c.$ What is the value of the following expression? $$
\{\{1 \ 1 \ 0\} \ [0 \ 1] \ 0\}
$$
  1. $\dfrac{2}{9}$
  2. $\dfrac{5}{18}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{7}{18}$
  5. $\dfrac{2}{3}$