2013 AIME II Problems/Problem 1

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 .