During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

How many times in twelve hours do the hands of a clock form a right angle? Use the + and - buttons below to move the hands of the NRICH clock, then click on the right angle symbol to check your answer.

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.

Key questions

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 $4$?

Possible extension

Learners could find out the times for $24$ hours and record using $24$ hour digital notation.

Possible support

Suggest counting round a clock, or using the interactive clock in the question.