Back in Time
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?
Age
14 to 16
Challenge level
Problem
Image
When she looked at the clock at 13:08, she noticed that the reflected display also read 13:08, as shown.
How many times in a 24-hour period do the display and its reflection give the same time?
Student Solutions
The only digits which will appear the same when reflected in the glass table-top are $0, 1, 3,$ and $8$. So it it necessary to find the number of times in a $24$-hour period that the display on the clock is made up only of these digits.
There are two possibilities for the first digit: $0$ or $1$.
There are four possibilities for the second digit: $0$, $1$, $3$ or $8$.
There are three possibilities for the third digit: $0$, $1$ or $3$.
There are four possibilities for the fourth digit: $0$, $1$, $3$ or $8$.
To find the total number of possible times, we can multiply together the number of possibilities for each digit.
Therefore the display and its reflection give the same time on
$2 \times 4 \times 3 \times 4 =96$ occasions