Reflected clock
Weekly Problem 42 - 2009
Beatrix has a 24-hour digital clock on a glass table. How many times in a 24-hour period will the display and its reflection give the same time?
Beatrix has a 24-hour digital clock on a glass table. How many times in a 24-hour period will the display and its reflection give the same time?
Age
7 to 14
Challenge level
Problem
Beatrix has a $24$-hour digital clock on a glass table-top next to her desk. When she looked at the clock at $13$:$08$ she noticed that the reflected display also read $13$:$08$.
Image
How many times in a $24$-hour period do the display and its reflection give the same time?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
The only digits which appear the same when reflected are $0$, $1$, $3$ and $8$, so we want to find the number of times the display on the clock is made up of these digits.
The first digit can be $0$ or $1$, the second digit can be $0$, $1$, $3$ or $8$, the third digit can be $0$, $1$ or $3$ and the fourth digit can be $0$, $1$, $3$ or $8$. Therefore there are $2\times 4\times 3\times 4=96$ different possible displays that are the same when reflected.