This problem is one which could be done as an introduction when extending or revising work on time and clocks. It will encourage the use of digital times.
At what time is the first right angle after 12 o'clock?
Why is it not just 15 minutes later?
Can you write down these times using digital notation
Why is the number of times not divisible by 4?
Learners could find out the times for 24 hours and record using 24 hour digital notation.
Using a geared clock would be helpful. (Some 'play' clocks allow you to move the minute and hour hands separately, which can lead to the hands being placed in an impossible way!)