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'The Mad Hatter's Watch' printed from

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The hour hand on the Mad Hatter's watch moves at the correct speed, but the minute hand moves one and a half times as fast as it should. Yesterday, it showed the correct time at 3 p.m. When did it next show the correct time?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

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This problem is taken from the UKMT Mathematical Challenges.