Two watches, one of which gains 1 min. and other looses 1 min. daily, were set correctly at noon on the first January 1978. When did the watches indicate the same time after January 1978?

The difference in time between the two watches increases at a combined rate of 2 minutes per day, since one gains 1 minute and the other loses 1 minute daily. For the two watches to indicate the same time, their times must differ by exactly 12 hours, which is 720 minutes. Using the formula 720 divided by the combined daily error of 2 minutes, we find it takes exactly 360 days. Adding 360 days to the starting time of noon on January 1, 1978, which is a leap year, brings the date to noon on December 26, 1978.

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