Reading from Behind
Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?
Age
11 to 14
Challenge level
Problem
The ten digits of a digital clock are shown below.
Image
I have a 12 hour digital clock which shows the time, using four digits, on a piece of glass, so it can be seen from both sides.
At what time between 3 o'clock and 10 o'clock will the time look the same from both sides?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Reading the digits from behind is the same as reflecting them in a vertical line of symmetry. This means $0$ and $8$ are read as themselves, and $2$ and $5$ are swapped. Note that the digits are read in the opposite order
Since the time is before 10:00, the first hour digit must be a 0. When read from behind, this means the last digit must also be a 0.
Since the time is between 3:00 and 10:00 and the second hour digit must be one that reads backwards as another digit, it must be either 5 or 8.
Since 08:80 is not a valid time, the time must be 05:20.