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IMAS 2015 Junior Division — Round 1 Question 9

IMAS · IMAS 2015 Junior Division — Round 1

Question 9

A group of students are staying in a hotel. If five of them share a room, then there is no room for six of them. If six of them share a room, there are just enough rooms, one of which has less than six students. Of the following five numbers, which cannot be the number of students?
  1. 46
  2. 51
  3. 56
  4. 61
  5. 66