Three of a Kind
How long is it between 5:55 and the next time all three digits on a digital clock are the same?
Age
11 to 14
Challenge level
Problem
The time shown on a digital clock is 5:55.
How many minutes will pass before the clock next shows a time for which all the digits are the same?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 316, or 5 hours 16 minutes
The digits will next be all the same at 11:11
5:55 to 6 = 5 minutes
6 to 11 = 5 hours
11 to 11:11 = 11 minutes
5 hours + 5 minutes + 11 minutes = 5 hours 16 minutes or 5$\times$60 + 16 = 316 minutes