This week’s Puzzle Corner activity is a simple problem with surprising results. The question posed in the puzzle is: “How many times during a day (24 hours) do the hour and minute hands of a clock point in the same direction?” The obvious answer seems to be 24, yet this is not correct. Students are challenged to make a guess and then use a clock to check the guess. They will need to do this carefully to find the correct answer.

Time Marches On works best with students who are comfortable telling time on an analog clock. You will find that even older students who are proficient at telling time need to have a clock available. Students need to actually turn the hands of a clock as they make a record of the number of times the hands coincide, otherwise they will not get the correct answer.

Since it may not be practical to have one clock per student, you may want to have students work in groups. A letter to parents asking to borrow small travel alarm clocks should get enough ciocks to use with groups. An alternative is to place one clock in a center and have students rotate through the center.

There are many possible extensions to this activity. One is to see how many times the second hand and the minute hand of a clock coincide in an hour. Another is to look at the time intervals between each coincidence of the minute and hour hands. In addition. students should be challenged to come up with their own extensions to this activity.

How many times during a day do the hour and minute hands of a clock point in the same direction?

Make a guess and write it below?

Now, get a clock and check your guess. What did you find out?

**Solution**

Click the arrow below to view the solution.

Have you tried doing this activity with a clock? It will help you get the correct answer, and is the best way to “see” why the answer is 22.

The approximate times at which the hands would coincide in a 24 hour period are listed below: (the .5 denotes half a minute)

- 12:00
- 1:05
- 2:10.5
- 3:15.5
- 4:21
- 5:26.5
- 6:31.5
- 7:37
- 8:42.5
- 9:48
- 10:54.5
- 12:00
- 1:05
- 2:10.5
- 3:15.5
- 4:21
- 5:26.5
- 6:31.5
- 7:37
- 8:42.5
- 9:48
- 10:54.5

**The answer is therefore: 22!**

The next 12:00 would begin the next 24 hour day.