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A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

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On Time

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

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Hand Swap

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?

Weekly Problem 45 - 2007

Stage: 3 and 4 Challenge Level: Challenge Level:1
At 8 o'clock, the obtuse angle between the hands of the clock is 120°. In the following six minutes, the minute hand turns through an angle of 36° whilst the hour hand turns through an angle of 3° in the same direction (clockwise!). So the obtuse angle between the hands increases by 33°, to 153°.

This problem is taken from the UKMT Mathematical Challenges.

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