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Summing Consecutive Numbers

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Night Watchmen

Stage: 3 Short Challenge Level: Challenge Level:1
The two watches will next agree when Granny's watch has gained twelve hours relative to Grandpa's watch. Each hour, Granny's watch gains one hour relative to Grandpa's watch, so it will take 12 hours for this to happen. At this time, both watches will show a time of 6 o'clock.

This problem is taken from the UKMT Mathematical Challenges.