## 196. Math Puzzle $9 / 81$

In a house, there are three clocks. On January 1st, they all showed the exact time. However, only the first clock was correct, the second clock lost one minute per day, and the third clock gained one minute per day.

After how much time will all three clocks, if they continue to run this way, show the correct time again?
According to the conditions, there is a difference of one minute per day between the correct clock and the other two. This means that after 60 days, a difference of 60 minutes will have occurred.

The necessary twelve-hour difference is achieved after 720 days, as 12 hours equal 720 minutes. This means that the clocks will show the same time again after exactly 720 days.

For some digital clocks with a 24-hour display, this time is doubled, as they only show the same time again after 24 hours. For such clocks, 1440 days would be required for all three to show the correct time again.