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How many times a day do the hour hand and minute hand of a 24-hour clock perpendicular to each other?
This is an examination question for my primary school to enter junior high school.

As we all know, the hour hand and the minute hand coincide 22 times a day.

It is convenient to consider every 12 hour.

When the hour hand turns, it is 12 hour, and it will coincide with the minute hand every few minutes, and this "extra minute" cannot exceed 59 minutes. So it is 1 1 coincidence. Double is 22 times.

In other words, considering the coincidence of the three stitches, choose the answer from the previous 22.

It is not difficult to find that all time points are XX:XX, such as 1:06. There won't be any 1: 06, xx seconds.

So it is very simple, only hours, that is, 12 or 0, can meet the requirements, that is, 2.

But throughout the ages, people prefer to leave simple methods behind and choose complex answers.

Some people in the comments section. Isn't it cold to stand at the moral high ground? Knowing the world is power. Who are you to say that my answer is wrong? It is obvious that primary school students do not have the ability of number theory. No matter how complicated this problem is, it is enough to solve it with junior high school mathematics. Your criticism of "inaccuracy" is purely because primary school students have never learned irrational numbers. I deliberately said, "It is not difficult to find that all time points are XX:XX, such as 1:06. There won't be any 1: 06 xx seconds. " .

Not all topics should be "emptied". Solve primary school problems with number theory and respect yourself.

Besides, there is something wrong with your settings. The two settings are the original clock, that is, the second hand goes once a second. Just change the soup without changing the medicine. You only need to set the second hand to walk once a second, or more precisely: the rotation of the minute hand and the hour hand is based on the rotation of the second hand. No matter how gorgeous your operation is, the answer is always twice. No matter how you say my answer is wrong, you have a problem.

The key to answering the question is to get to the core, you are far from it. Complete "problem solving" thinking. It can be said that your idea of solving this problem is completely wrong, but the answer is correct, and the python program in the back row has proved it.