How many times in a day do the three hands of a watch coincide exactly?

Because the hour, minute, and second hands all rotate on the same axis, they all have their own angular velocities, and there is a certain relationship between their angular velocities. Based on this relationship, we can solve this problem. If the angular velocity of the hour hand is W, the minute and second hands are 12W and 720W respectively.

First, let's examine the angle of the hour hand and the minute hand when it coincides, and set it to x. Then there is the equation: x w = (x + n*360) 12w where n is the number of turns the minute hand exceeds the hour hand.

The value of n can range from a positive integer between 1 and 22. Only 22 was taken because the minute hand traveled 24 times in a day, but the hour hand also traveled twice. So 24-2=22.

Then, we can substitute the n value to find x. After finding x, it also depends on whether the second hand is also at x at this time. It can be seen that the time taken for the hour hand to go to x is x w, and the total angle of the second hand is 720w * x w = 720x.

Then simplify this value to within 360 to see if it is w. The simple process is as follows: when n = 1, x = 360 11.

720 * 360 /11 ——5*360/11。It can be seen that the hour hand coincides with the minute hand, and the hour and second hand do not coincide with them. When n = 2, x = 2*360 11.

720*2*360/11 ——10*360/11。The second hand does not coincide. When n = 3, x = 3*360 11.

720*3*360/11 ——4*360/11。The second hand does not coincide. Have a regular and see the ......... for yourselfWhen n = 11, x = 11*360 11 = 360.

720*360 ——360。The second hand coincides, and it is 12 noon. Cycle .........From the above, it can be seen that there are two times in a day when the three stitches completely coincide, at 12 noon and 0 am.

24 times, once an hour. 24(0):00:00（12：00：00） .

The second hand rotates once, the minute hand jumps one square, the minute hand rotates once, the hour hand jumps one square, and the second hand goes one square for each revolution, and the minute hand goes one square to indicate one minute; For every 12 moves of the minute hand, the hour hand moves one block to indicate 12 minutes; As long as the minute and hour hands coincide, the second hand will certainly coincide with them within 1 minute; So consider the minute and hour hands.

It coincides at 0:00, and everyone knows this.

1:05 coincides once: everyone knows 1:

At 00, the hour hand means "1", and for the minute hand, "1" means 5 minutes, so at 1:05, the minute hand means "1"; The hour hand did not move compared to 1:00, because it was less than 12 minutes, and the hour hand did not move one square until 12 minutes, so the two coincided at this time, and if the second hand is counted, the exact time is 1:

At 05:05, the second hand moves for 5 seconds, and the other two do not move, so the three coincide.

2:10 coincided, and 10 minutes was still less than 12 points.

3:16 coincides, 16=15+1;Because at 3:12 the hour hand moves one square, the minute does not coincide with it until it reaches 16; And so on, and the next coincidence time is:

5:27 (The hour hand goes 1 time at 5:12 and 5:24 and moves 2 squares, so 5:25 + 2 minutes = 5:27).

11:59 (11:59:59 The three needles will coincide once stupidly, at first I didn't believe it, thinking that it was impossible; But facts speak louder than words, you can observe it once---don't wait stupidly, you can dial the clock, and then dial it correctly after observing)

12:00 (again).

13:05 (same as previous analysis).

0-23, once each, for a total of 24; Remember that 24:00 can't be counted, if you can count it, the previous 0:00 is yesterday;

The 22 times were: 0:00, 1:60 11, 2:120 11, 3:180 11, 4:240 11, 5:300 11, 6:360 11, 7:420 11, 8:480 11, 9:540 11, 10:600 11......Two times each.

Since the angle of the center of the circle rotated by the hour hand in 1 minute is in degrees, the angle of the center of the circle in which the minute hand rotates in 1 minute is 6 degrees. When the two needles coincide for the first time and then the second time, the angle of the circle center rotated by the minute hand more than the hour hand is 360 degrees. Therefore, the time required for the two pins to coincide again is x:

x = 720 11 (minutes).

That is, 720 11 minutes, that is, 12 11 hours, the minute hand catches up with the hour hand once.

Number of coincidences in a day:

24 * 60 (720 11) = 1440 * 11 720 = 22 times.

Overlapping 24 times in a day.

The times are:

First of all, understand that it takes 60 minutes for the minute hand to make one revolution, so its angular velocity is 360 degrees for 60 minutes, that is, 6 degrees for minutes;

One rotation of the hour hand is 12 hours, and the angular velocity is 360 degrees for 12 hours, that is, degree minutes;

Assuming that the starting time is zero, which coincides at this time, and the elapsed time t (minute) coincides again, and the minutes go one more turn than the time, and so on, assuming that the number of revolutions the hour hand has traveled is n, the following formula can be obtained;

6 (degrees min) t (minutes) - (n-1) (circle) * 360 (degrees) = degrees minutes) t (minutes) -- the left side of the equation is the angle at which the minute hand travels, and the right side is the angle at which the hour hand walks; There are 24 hours in a day, so n<=24

The above equation is simplified, i.e., t=360(n-1);

n=1,2,3.... are calculated separately24 Calculate the coincident time point (assuming the pointer rotates linearly, ignoring the case of one block (one second) at a time).

It's definitely not, it takes one-half of a degree to turn the hour hand for one minute.

It takes 6 degrees for the minute hand to turn for one minute.

You need to use reading books to draw pictures and calculate.

For example, at 1:05, it takes 30 degrees for the minute hand to turn for 5 minutes, and the hour hand needs to be in degrees. But don't forget, the minute hand turns from 12 to 1, and the hour hand starts at 1! The final hour hand should be pointing in!

So the hour and minute hands must not coincide at 1:05! And so on, and your answer is incorrect

The minute hand must coincide with the hour hand once for each revolution, and if it coincides at 12 o'clock, it will coincide at 1:5 o'clock. Divide is also a point ... All the way to the minute. Don't you have a watch?

1. Reason:

1. The rotation point of the hour hand and minute hand is in the same position, which is like the center of two concentric circles; The hour and minute hands are like the terminal edges of the angles, and the coincidence, which means that the terminal edges of the two rotating angles coincide.

2. Common sense: The angle at which the minute hand travels per minute is 6°, and the angle at which the hour hand travels per minute is (according to the adjacent digits of the 12 numbers from 1 to 12, that is, 2, 2, 3,..Between the two numbers like 11 12, the hour hand travels 5 minute squares, and the minute hand travels through a circle on the surface, i.e. 12 5 = 60 minute squares.

Therefore, at the same time, the hour hand only goes to 5 60 = 1 12 i.e. 6° (1 12) =.

3. The angle between two o'clock is 30° every 1 hour. coincides, then there is:

|Minutes Angle of the minute hand per minute - minutes The angle of the hour hand per minute - the angle at which the hour is located|=0】

Reduced to |Again: x, minutes; n hour, n = 0, 1 o'clock 、..23 o'clock].

For example, if 8 o'clock and 9 o'clock coincide there, solution.

Get x=240 minutes=43 minutes and 38 seconds.

At 8:43:38, the hour and minute hands coincide.

2. The time of the hour and minute hands of the day coincides as follows (the time form is hour: minute: second):

coincides 22 times a day, every 65 and 5/11 minutes;

Note: 00:00:00 and 12:00:00

The hour hand turns 2 times a day, the minute hand turns 24 times, and they meet 22 times (the minute hand runs faster than the hour hand) 24 22 = 12 11 = 1 and 1 11 hours.

So the time of the encounter.

12：00：00；(Ibid. hereinafter).

Overlapping 24 times in a day.

The times are:

Upstairs is right, you can catch up with the hour hand once in more than an hour, and it can coincide 24 times a day.

Wrong, 11:55 doesn't coincide, it doesn't coincide until 12:00, so it's 22 times.

The hour and minute hands coincide 22 times a day, and counting 00:00 in the morning, it is 23 times, and it is impossible to have 24 times.

When the minute hand is turning, the hour hand cannot stop in place and will rotate, so the overlap time is wrong.

There is a formula m=(60 11)xn n n which refers to the hour hand (1··· 11) M refers to the minute hand.

It is calculated that there is no 11:55 and 23:55 (n is 11, m is 60, is 12:00 and 24:00).

Therefore, 11:55 and 23:55 are abolished and 24:00 is added as the final correct coincidence, and there are 23 in total.

If you still have doubts, you may wish to take the watch and look around for yourself (

How many times do the minute and hour hands coincide from 0:00 (inclusive) to 24 (exclusive) in a clock?

Answer: (1) The first time it coincides at 0 o'clock; (2) From the last coincidence, the minute hand can only catch up with the hour hand for more than 60 minutes, that is, there can only be one chance of overlap at most every hour. There is no chance of overlapping between 0 o'clock (exclusive) and 1 o'clock, and between 11 o'clock and 12 o'clock (exclusive), so these two periods can coincide 11 times together; (3) Similarly, there are 11 chances of overlapping between 12 o'clock (inclusive) and 24 o'clock (exclusive).

Thus, the minute and hour hands coincide 22 times.

It is impossible to overlap. There's no time to overlap or anything.

How many times in the 24 hours of the day do the hour, minute and second hands of the clock coincide exactly?

11 2 = 22 times.

1 o'clock, 13:30 (another 5 11 minutes.)

2 o'clock, 2 p.m. 60 p.m. (10 11 p.m.)

3 o'clock, 15:90 (4 11 minutes.)

4 o'clock, 16 o'clock 120 (again 9 11 minutes.)

5 o'clock, 17 o'clock 150 (again 3 11 minutes.)

6 o'clock, 18 o'clock 180 (again 8 11 minutes.)

7 o'clock, 7 p.m. 210 (again 2 11 minutes.)

8 o'clock, 20 o'clock 240 (again 7 11 minutes.)

9 o'clock, 21 o'clock 270 (again 1 11 minutes.

10 o'clock, 22 o'clock 300 (again 6 11 minutes.)

12 o'clock and 24 o'clock.

"0" (not counted) to "24" overlap 2 times, once at 12 o'clock and once at 24 o'clock.

The second hand rotates once, the minute hand jumps one square, the minute hand rotates once, the hour hand jumps one square, and the second hand goes one square for each revolution, and the minute hand goes one square to indicate one minute; For every 12 moves of the minute hand, the hour hand moves one block to indicate 12 minutes; As long as the minute and hour hands coincide, the second hand will certainly coincide with them within 1 minute; So consider the minute and hour hands.

It coincides at 0:00, and everyone knows this.

1:05 coincides once: everyone knows 1:

At 00, the hour hand means "1", and for the minute hand, "1" means 5 minutes, so at 1:05, the minute hand means "1"; The hour hand did not move compared to 1:00, because it was less than 12 minutes, and the hour hand did not move one square until 12 minutes, so the two coincided at this time, and if the second hand is counted, the exact time is 1:

At 05:05, the second hand moves for 5 seconds, and the other two do not move, so the three coincide.

It coincided at 2:10 a.m., and 10 minutes was still less than 12 minutes.

3:16 coincides, 16=15+1;Because the hour hand moves one block at 3:12, the minutes do not coincide until 16; And so on, and the next coincidence time is:

5:27 (The hour hand goes 1 time at 5:12 and 5:24 and moves 2 squares, so 5:25 + 2 minutes = 5:27).

11:59 (11:59:59 The three needles will coincide once, and at first I didn't believe it, thinking that it was impossible; But facts speak louder than words, you can observe it once---don't wait stupidly, you can dial the clock, and then dial it correctly after observing)

12:00 (again).

13:05 (same as previous analysis).

0-23, once each, for a total of 24; Remember that 24:00 can't be counted, if you can count it, the previous 0:00 is yesterday;