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IMAS 2011 Junior Division — Second Round Question 7

IMAS · IMAS 2011 Junior Division — Second Round

Question 7

A Youth Hostel has twenty-one rooms numbered from 1 to 21. To conceal their identifies from outsiders but not from the staff, the keys are assigned two-digit codes. The first digit is the remainder when the room number is divided by 3, and the second digit is the remainder when the room number is divided by 7. For instance, the key to room 8 has the code 21. Which room has the key with the code 12?