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jmc

number theory junior

Problem

It is now 12:00:00 midnight, as read on a 12-hour digital clock. In 122 hours, 39 minutes and 44 seconds the time will be . What is the value of ?
Solution
Since the clock reads the same time every 12 hours, we find the remainder after dividing 122 hours by 12 hours, which is 2 hours. Counting forward from midnight, the clock will read 2:39:44, so .
Final answer
85