I fear the answer is beyond my brain power but will have a think about it. I don't think 11:08pm on a Saturday night is the best time for my brain to be answering maths problems!

Is that an ambiguous time by the way?

]]>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.

]]>Except when they line up exactly which will be 11 times (once per hour) if 12 o'clock doesn't count.

So my answer is 3589 out of a possible 3600 seconds are ambiguous.

I'm bound to be missing something, I'm never any good at puzzles!

]]>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.

]]>Imagine a two-handed analogue clock (hour and minute hands) where the two hands are indistinguishable, i.e. they are the same size, shape, colour, depth and so on.

During any 12-hour period, at how many different times is the time shown by the clock ambiguous?

NB: 12 o'clock doesn't count.