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Hanoi Open Mathematics Competition 2016 Senior Question 2

HOMC · Hanoi Open Mathematics Competition 2016 Senior

Question 2

The numbers \(A=(672,673,674,\ldots,2016)\) are on a table. At each step, three arbitrary numbers \(a,b,c\) currently on the table are replaced by \(\frac13\min(a,b,c)\). After 672 steps, only one number \(m\) remains. Which assertion holds?
  1. \(0\lt m\lt 1\)
  2. \(m=1\)
  3. \(1\lt m\lt 2\)
  4. \(m=2\)
  5. None of the above.