How Many Times do The Hands of a Clock Coincide in Day

Introduction

In an entire day, the hands of a clock will coincide 22 times. Some interview questions are unexpected. A good illustration of this is the query, "How many times do the hands of a clock cross each other in a day?" The interviewer is only sometimes looking for a quick response. Instead, potential employers want to know if you can solve problems and develop a workable solution.

Although it might be tempting just to say "24," the right response is "22." This can be inferred from the fact that the clock hands overlap twice daily at 12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, 8:40, 9:45, and 10:50.

Since the minute hand is at 11 and the hour hand is moving toward 12, there won't be an 11:55 because the hands won't overlap at that time.

Explanation

A clock's hands line up 11 times every 12 hours (between 11 and 1, they only line up once, at midnight).

The table given below shows the time of the collisions of the hands.

AM

12:00

1:05

2:11

3:16

4:22

5:27

6:33

7:38

8:44

9:49

10:55

PM

12:00

1:05

2:11

3:16

4:22

5:27

6:33

7:38

8:44

9:49

10:55

Instead of every 60 minutes, the hands cross over about every 65 minutes.

∴ Every day, the hands line up 22 times.

Now here are some questions you may be asked during an interview. Such questions will not only test your aptitude but also your perceptive skills and your ability to solve problems accurately.

A clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 p.m.?

The hour hand rotates by 30° for each hour. When the hour hand moves from 8 to 2 o'clock, it makes an angle rotation of 6 hours, or 180°.

Similarly, if you were asked, “How many times a day are a clock's hands perpendicular?”

The clock's hands will be at right angles to one another twice between 11 o'clock and 1 o'clock in 12 hours, but 22 times in a single hour. This is in contrast to the clock's hands being at right angles to one another twice between 11 o'clock and 1 o'clock. They will thus be at right angles to one another 44 times in a 24-hour hour.