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jmc

number theory junior

Problem

The time right now is 9 o'clock. On a 12-hour clock, what time will it be 2004 hours from now?
Solution
Note that 2004 is divisible by 4, since the last two digits, 04, form a multiple of 4. Also, 2004 is divisible by 3 since the sum of the digits, , is a multiple of 3. Therefore, 2004 is a multiple of 12, and 2004 hours from now it will be o'clock again.
Final answer
9