Clock Hands Overlap Answer: 22 Times [Solved]

Answer: The hands of a clock overlap 22 times in a day.

The clock hands overlap answer is 22 times in a day, not 24. The minute hand gains on the hour hand at 5.5 degrees a minute, so the hands meet every 65 minutes and 27 seconds. Here are all 11 overlap times and the trap that catches candidates.

The Puzzle

Imagine an analog clock set to 12 o’clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?

This is a classic Microsoft interview question, and it has survived because the obvious answer is wrong. Most candidates say 24, reasoning that the hands meet once an hour. The walkthrough below shows where those two missing overlaps go.

Why the Clock Hands Overlap Answer Is 22, Not 24

The whole puzzle turns on one fact: the hour hand does not stand still while the minute hand chases it. Every time the minute hand completes a lap, the hour hand has moved on, so the catch-up takes a little longer than an hour. Work through the speeds and the answer falls out on its own.

Step 1: How fast each hand moves

The minute hand sweeps the full dial in 60 minutes, so it moves at 360 degrees divided by 60, which is 6 degrees a minute. The hour hand takes 12 hours, or 720 minutes, to sweep the same dial, so it moves at 360 degrees divided by 720, which is 0.5 degrees a minute. Those two speeds are all you need.

Step 2: How fast the minute hand gains

Since both hands move in the same direction, what matters is the gap between their speeds. The minute hand gains 6 minus 0.5, which is 5.5 degrees a minute, on the hour hand. For the hands to overlap again, the minute hand must gain a full lap of 360 degrees. Divide 360 by 5.5 and you get 65.4545 minutes, which is 65 minutes and about 27 seconds. So the hands overlap every 65 minutes and 27 seconds, not every 60 minutes.

Step 3: From one overlap to the next

Start at 12:00 with the hands together. After 65 minutes and 27 seconds the minute hand has gained exactly one lap, and the hands meet again at about 1:05:27. After another gap they meet at about 2:10:55. Each meeting lands a little later in the hour than the last, which is why the times drift from 1:05 to 2:11, 3:16, and so on: the hour hand keeps moving, so each meeting slips a few minutes later.

Step 4: From 12 hours to a full day

Twelve hours hold 720 minutes. Divide 720 by 65.4545 and you get exactly 11. So the hands overlap 11 times in 12 hours. A day holds two 12-hour cycles, and 11 times 2 is 22. That is the full calculation, and it uses no guessing at all.

The Exact Overlap Times

The table below lists every overlap in a 12-hour cycle, starting at midnight. The same 11 times repeat in the afternoon and evening, giving 22 overlaps in a full day. Note that midnight counts once: it opens the day, and the next midnight opens the following day.

Overlap	Time	What to notice
1	12:00:00	The hands start together at the top of the dial.
2	1:05:27	The first catch-up, just past 1:05.
3	2:10:55	The meeting time has slipped to almost 2:11.
4	3:16:22	Past the quarter hour now.
5	4:21:49	Approaching the 22-minute mark.
6	5:27:16	Just past 5:27.
7	6:32:44	Just past 6:32.
8	7:38:11	Just past 7:38.
9	8:43:38	Just past 8:43.
10	9:49:05	Just past 9:49.
11	10:54:33	The last overlap before noon, just before 10:55.

Now look at what happens between 11:00 and 1:00. There is no overlap near 11:05, because by the time the minute hand reaches the 11, the hour hand has already moved past it toward 12. The minute hand finally catches the hour hand at 12:00 itself. That is why the count is 11 per cycle instead of 12: the 11 o’clock overlap and the 12 o’clock overlap are the same event. Lose sight of that, and you overcount by one per cycle, which is exactly how 22 becomes 24.

The Trap Most Candidates Fall Into

The most common wrong answer is 24, from counting one overlap per hour. The second trap is subtler: rounding the gap to 65 minutes and dividing 1,440 minutes by 65 gives 22.15, which rounds to 22. That lands on the right number for the wrong reason, and an interviewer who asks for the exact times will catch it at once. The exact gap is 65 minutes and 27 seconds, and with that gap the count comes out at exactly 22, with nothing left over.

A third trap is answering 1:05 for the first overlap after 12:00. At 1:05 exactly, the minute hand points at the 1, but the hour hand has crept a little past the 1, so the hands have not quite met. The true meeting time is 1:05:27. In an interview, giving the seconds shows you did the relative-speed calculation instead of guessing from the dial.

What the Interviewer Is Testing in the Clock Hands Overlap Answer

This question tests four things at once, and the answer alone proves none of them. First, it tests whether you model a moving target instead of a fixed one: the hour hand moves, and candidates who freeze it get 24. Second, it tests relative speed, a tool that shows up across scheduling, rates, and catch-up problems in real work. Third, it tests off-by-one discipline: counting the shared 12:00 overlap twice is the same class of error as double-counting a boundary in a report. Fourth, it tests whether you can explain a result clearly, with the speeds, the gap, and the count in that order, instead of jumping to a number you half remember.

The strongest way to answer in the room is to start with the two speeds, state the 5.5-degree relative speed, compute the 65-minute-and-27-second gap, and then divide 720 by that gap to get 11 per 12 hours and 22 per day. That path takes under a minute and gives the interviewer a natural opening to ask for the exact times.

Try These Follow-Up Questions

Interviewers often keep going once you answer 22. The three follow-ups below use the same relative-speed idea, so they are worth preparing before you walk in.

How many times do the hands point in exactly opposite directions? The hands are opposite when the minute hand is half a lap, or 180 degrees, ahead. At 5.5 degrees a minute, that first happens after 180 divided by 5.5, which is about 32 minutes and 44 seconds, at roughly 12:32:44. After that it repeats every 65 minutes and 27 seconds, giving 11 times per 12 hours and 22 times a day, the same count as the overlaps.

How many times do the hands form a right angle? A right angle happens twice per overlap cycle: once when the minute hand is 90 degrees ahead, and once when it is 270 degrees ahead. That doubles the count to 22 per 12 hours and 44 times a day.

How many times do all three hands line up exactly? If the clock has a smoothly sweeping second hand, the three hands line up exactly only at 12 o’clock itself, at midnight and at noon. Every other hour-minute overlap falls on a fraction of a second, so the second hand is never exactly on top of the other two. This is a good answer to give with a smile, since it shows you checked the edge case instead of assuming it.

Quick Answers to Common Questions

How many times do clock hands overlap in a day?

They overlap 22 times in a day: 11 times in each 12-hour cycle.

Why not 24 times, once an hour?

Because the hour hand moves while the minute hand chases it, each overlap takes 65 minutes and 27 seconds. Between 11:00 and 1:00 the hands meet only once, at 12:00, so one overlap per cycle disappears from the naive count.

What is the first overlap after 12:00?

The first overlap after 12:00 is at about 1:05:27, not at 1:05 exactly.

How many times do clock hands overlap in a week?

Multiply the daily count by 7: 22 times 7 is 154 overlaps in a week.

Try Another Puzzle

If you liked this one, try the Goldman Sachs clock angle puzzle at 11:55, which asks for the exact angle between the hands instead of the count. Then test yourself on the hourglass puzzle that measures exactly 9 minutes, and on the Monty Hall problem, where switching doors doubles your odds.