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SMO 2005 Junior Round 1 Question 10

SMO · SMO 2005 Junior Round 1

Question 10

Suppose $3$ distinct numbers are chosen from $1,2,\ldots,3n$ with their sum equal to $3n$. What is the largest possible product of those $3$ numbers?
  1. $n^3-n$
  2. $n^3$
  3. $n^3+n$
  4. $n^3-7n+6$
  5. $n^3-7n-6$