Problem number 20. There are five clocks on the wall. It is known that one clock is an hour fast, one clock is an hour slow, one clock shows the correct time, and two clocks have stopped. Which clock shows the correct time? From the problem, we know that there's a clock that shows the correct time, and then there's a clock that's an hour fast, so it will show an hour after that time, and one clock that's an hour slow, so it will show an hour before that time. That means that there are three clocks that show times that are exactly an hour apart. If the clocks show the time on the hour, we could have something like one o'clock, two o'clock, or three o'clock, or seven o'clock, eight o'clock, and nine o'clock. But if the time is not on the hour, we might have something like 3.15, 4.15, and 5.15, or 7.28, 8.28, and 9.28. Of those times that are an hour apart, the middle one will be the correct time. Let's see if we can figure it out by writing down the times that the clocks show. Clock A shows six o'clock. The hour hand is here, and the minute hand is pointing to 12. Clock B is showing two o'clock. Clock C is showing four o'clock. Clock D is showing three o'clock. Clock E is showing seven o'clock. All these clocks are pointing exactly at the hour. And of the point times in order, we have two o'clock, three o'clock, four o'clock, six o'clock, and seven o'clock. Of these, two o'clock, three o'clock, and four o'clock are in order. Three o'clock would be the correct time because then we have one clock that's an hour slower, that's the two o'clock, and the four o'clock is an hour fast. The other clocks, six and seven, would be the ones that are stopped. So the clock that's showing the correct time is the clock that shows three o'clock, which is clock D.

clock puzzle

correct time

consecutive times

stopped clocks

time identification