It’s not uncommon nowadays for people to be asked how many times an hour and minute hand meet in a day when going through an interview for a job, in fact, it’s slowly becoming one of the most popular interview questions.
This is because the question allows hiring managers or interviewers to see if the interviewee can come up with reasonable, rational solutions when faced with a problem, and to see how they formulate these solutions.
While the interviewer won’t be looking for the exact answer, giving them the correct one definitely won’t hurt your chances of getting hired.
While it might be your first instinct to answer 24 to the question, the correct answer is actually 22.
The hands will overlap at 12:00, 1:05, 2:10, 3:15, 4:20. 5:25, 6:30, 7:35, 8:40, 9:45, 10:50, and since those 11 times happen twice in a day, the hands of your watch will meet 22 times.
The only hour in which the hands won’t meet would be the 11th hour. This is because, when it’s time for the minute hand to approach the 55-minute marker, the hour hand will already be closer to the 12 o’clock marker than the 11 o’clock marker.
Coming up with that answer was fun enough, but figuring out the formula is a different kind of fun.
In one hour, the long hand would have finished one lap around the dial while the hour hand would complete 1/12th of a lap.
So that means that in x hours, the long, minute hand will finish x laps, while the hour hand will complete x/12 laps. When the hands meet for the first time, the minute hand would have completed one more lap than the short, hour hand, and the second time they meet the minute hand would have finished two more laps, and so on and so forth.
This can give us the equation that x= x/12 + N, with x being the number of hours and N being the number of times the hands overlap, and since a day has 24 hours, the equation would look like this:
x = x/12 + N
-N = x/12 -x
-N = 24/12 – 24
-N = 12 – 24
-N = -22
N = 22
So whether this question was asked at a job interview or at a party conversation, rest assured that you not only know the answer, but you know the math to back it up, too!