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It's simple: every 19 years.
Knowing why it's a little more complicated, I'll try to talk about it with my expertise.
The Gregorian calendar, which should be properly called the "Gregorian calendar", was promulgated by Pope Gregory XIII in 1582. In China, it is also known as "AD" and "Western Yuan".
The current version of the lunar calendar is the "Shixian Calendar" promulgated in 1644 by Prince Regent Dorgon. In fact, this calendar was revised with the help of Western missionaries during the Chongzhen period, and the reason for the change of dynasty was promulgated by the Qing Dynasty.
The two calendars were compiled on different principles. The Gregorian calendar is the "Gregorian calendar", which is based on the cycle of the Earth's revolution around the Sun. The Earth's orbit around the Sun is a day, also known as a "return year".
The Gregorian calendar sets a leap year every 4 years, that is, one more day in February, which becomes 366 days.
Although the lunar calendar is colloquially called "lunar calendar", it is not really a "lunar calendar", to be exact, it is a "lunisolar calendar". Because the months of the lunar calendar follow the moon, and the moon revolves around the earth for days, also called a "synodic month", so there are only two kinds of lunar months: 29 days and 30 days, and there will be no "in the Gregorian calendar". The year of the lunar calendar is based on taking into account the synodic month, and the solar terms are used to regulate yin and yang, so that the seasons will not be disordered, so the leap month of the lunar calendar is a whole month, and the year with a leap month is 13 months.
19 years is what people can observe and experience within their average life expectancy, and the Gregorian calendar and the lunar calendar "almost coincide".
The reason why I say "most likely to coincide" is because some of the 19-year Gregorian calendar and the lunar calendar coincide exactly, and some will be one day apart. The movements of celestial bodies are all irrational numbers, and rounding is also technical work!
The so-called "24 solar terms" were called "qi" in ancient times. In order to distinguish between them, in each month, the front is called "Seten" and the latter is called "Nakami". Elementary school math calculates that in 19 Gregorian calendar years, there should be 228 (12 19) solar terms and 228 neutral terms.
However, there will be 235 synodic months in the 19th year of the lunar calendar, and there will be 7 leap months in 19 years because the lunar calendar designates the month without neutral air as a leap month.
If you do the calculations,,, difference is less than a tenth of a day. The difference between two decimal places is why some years are one day different from 19 years ago, which roughly coincides! Mankind has done its best, and for the whole of this pile of irrational numbers, it has invented n kinds of calendars!
Seven leaps in 19 years, this law has been discovered in the Spring and Autumn Period of our country. The operation of the Copernican system is also the result of this. Zu Chongzhi's calculation is "144 leaps in 391 years", which is more accurate.
Modern timing and calendar calculations are more precise, with "leap seconds" as fine-tuning. In any case, the Gregorian calendar and the 19th year of the lunar calendar coincide once, which is still approximately accurate and can be referred to.
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You're talking about the college entrance examination, this probability is not large, it is estimated that it will happen once in decades.