Problem No. 1. Digital Clock

It is 7.30 now. How long should we wait until the digital clock uses the same digits to display the time?

Teacher tip

Good recreational problem for a "warm up" activity at the beginning of the class.

Solution

If it is 7.30 am and the clock uses 12-hour display, the next time displayed with the same digits is 3.07 pm, which is after 7 hours and 37 minutes; but if the clock uses 24-hour display, the next time displayed with the same digits is 0.37 am, which is after 17 hours and 7 minutes. If it is 7.30 pm, so the clock uses 12-hour display, and the next time displayed with the same digits is 0.37 am, which is after 5 hours and 7 minutes.