Nice try, but no.

Take 3 o'clock say. On a clock where the two hands are identical, 3 o'clock will look like 12:15, but not quite because at 12:15 the hour hand has moved a bit beyond the vertical. The trick is to find pairs of times where the hands *are* in exactly the same positions.

I hope that helps. Note also that I said a 12-hour period, so we don't need to worry about AM and PM.

studymaths wrote:

If the hands are indistinguishable isn't the time is always ambiguous?

No. At 3 o'clock, the minute hand is pointing vertically (on a bearing of 0° if you like) while the hour hand is pointing due east (bearing of 90°). There is no corresponding time where the hour hand is at 0° and the minute hand is at 90° (12:15 doesn't quite work because the hour hand has moved beyond 0°). So if one hand is pointing due north and the other is due east, you know it must be 3 o'clock.

However there are times when you can't tell.

Good luck with the GCSE teaching by the way - can't be an easy task for you. I did my GCSEs in 1996.

Plutoman, click on the 132 box to get the explanation.  I think I understand it!