Problem:
A particular -hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a , it mistakenly displays a . For example, when it is PM the clock incorrectly shows PM. What fraction of the day will the clock show the correct time?
Answer Choices:
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Solution:
The clock will display the incorrect time for the entire hours of , and . So the correct hour is displayed correctly of the time. The minutes will not display correctly whenever either the tens digit or the ones digit is a , so the minutes that will not display correctly are , and , and . This is of the possible minutes for a given hour. Hence the fraction of the day that the clock shows the correct time is .
The problems on this page are the property of the MAA's American Mathematics Competitions