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Tick's watch runs 2 minutes per hour too slow. Tock's watch runs 1 minute per hour too fast. They set them to the same time at noon on Sunday. The next time they met, one of the watches was one hour ahead of the other. What was the earliest time this could have been?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.