Problem:
Suppose that the measurement of time during the day is converted to the metric system so that each day has metric hours, and each metric hour has metric minutes. Digital clocks would then be produced that would read just before midnight, at midnight, at the former AM, and at the former PM. After the conversion, a person who wanted to wake up at the equivalent of the former AM would set his new digital alarm clock for , where , and are digits. Find .
Solution:
Under the current system, there are minutes in a day. AM is minutes after midnight. Because there are metric minutes in a day, the equivalent metric time is metric minutes after midnight. The new digital alarm clock should be set at , and the requested answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions