# Answer to Puzzle #5: Degrees Between the Hands of a Clock

5. How many degrees (if any) are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?

I worked this one out for myself too, this is one of the easier ones...

Before reading the answer can I interest you in a clue?

First consider the picture below:-

Clearly there is an angle between the hour and minute hand other than zero. This comes from the fact that the hour hand, having been exactly on the '3' at 3 o'clock, doesn't simply stay there whilst the minute hand is catching up. Rather it is one quarter of the way on it's journey to 4 o'clock. So let us consider the angles clockwise from 12 o'clock so.

12 o'clock = 0°
1 o'clock = 30°
2 o'clock = 60°
3 o'clock = 90°
6 o'clock = 180°

The simplest way to think of this is that each hour is made up of 30° and that the hour hand will have moved one quarter of an hour past three o'clock. ¼ x 30° = 7.5°

If you are interested in exactly what time the two hands overlap, when there zero degrees between them; I deal with this in Puzzle #35.

Victory for Bard on this one.

If you're curious what Bard made of this puzzle...

If you're curious what ChatGPT made of this puzzle...

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