Problem:
A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display?
Answer Choices:
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Solution:
The largest possible sum of the two digits representing the minutes is 14 , occurring at 59 minutes past each hour. The largest possible single digit that can represent the hour is 9 . This exceeds the largest possible sum of two digits that can represent the hour, which is . Therefore, the largest possible sum of all the digits is , occurring at 9:59.
The problems on this page are the property of the MAA's American Mathematics Competitions