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SMO 2022 Junior Round 1 Question 5

SMO · SMO 2022 Junior Round 1

Question 5

If $n$ can take the value of any positive integer, how many distinct values can the expression $$\left\lfloor\frac n4\right\rfloor-\left\lfloor\frac n7\right\rfloor-\left\lfloor\frac n{14}\right\rfloor-\left\lfloor\frac n{28}\right\rfloor$$ take?
  1. 1
  2. 2
  3. 3
  4. 4
  5. infinitely many