Everywhere 9

M: The number 9 is a number with many mysterious attributes. Do you know that every celebrity's birthday has a 9 hidden in it?

Please look at Washington's birthday. He was born on February 22, 1732. According to American custom, these numbers are written as a number 222 1732. Now, rearrange the numbers in this number to form any different numbers. Subtract a smaller number from a larger number to get a difference.

(For example: 2221732-1232272 = 989460)

M: Add up the figures of the difference. In this example, you get a total of 36. Three plus six equals nine!

M: If you do the above calculation for the birthdays of De Gore, John F Kennedy or any famous person, you will finally get 9. Is there any mysterious relationship between celebrities' birthdays and 9?

Once you understand the calculation program explained by the paradox above, you can try to let each student calculate his birthday in class. As a result, everyone finally got a 9.

If you add all the digits of a large number to get a sum, then add all the digits of this sum to get another sum, and then continue to sum the digits until the final digit sum is a digit, which is called the "digital root" of the original number. The root of this number is equal to the remainder of the original number divided by 9, so this calculation process is often called "nine-in-one method".

The quickest way to find the roots of a number is to omit 9 when adding the original numbers. For example, the first two numbers are 6 and 8, which add up to 14, and then add 4 to 1, and the result is 5. In other words, if the sum of the numbers after 9 is greater than-digits, add the two numbers again to calculate this sum. The last number is the desired number root. It can be said that several modules are equivalent to the original number pair 9, which is called module 9 for short. Because 9 is divided by 9 and remains zero, 9 and 0 are equivalent in the modulo 9 algorithm.

Before the invention of computers, accountants often used modulo 9 algorithm to check a large number of sums, differences, products and quotients. For example, if we subtract B from A to get C, the result can be checked as follows: subtract the digital root of A from the digital root of B to see if the difference is equal to the digital weight of C. If the original difference is correct, then the difference of the digital root is also correct. This does not prove that the original calculation is correct, but if the differences of several roots are not equal, the accountant will know that he has miscalculated. If several roots can match, the probability of his correct calculation is 8/9. This digital root test method can also be applied to addition, multiplication and division of numbers.

Now we can understand the mystery of the above birthday algorithm. Suppose a number n consists of many numbers. We get a new number n' by scrambling the number n. Obviously, n and n' have the same number. Therefore, if we subtract the two, we will get 0, which is the same thing as 9 (in the modulo 9 algorithm). This number, 0 or 9, must be the digital root of the difference between n and n'. In short, take any number, rearrange it into another number, and subtract them. The root of the difference is 0 or 9.

Only when n and n' are equal, the result is 0. Therefore, we should remind students that when calculating with their own birthdays, we must ensure that the rearranged numbers can get a difference. As long as two numbers are not equal, the root of the difference is 9.

You can do a lot of digital magic with this ubiquitous 9. For example, when a student writes a number when the teacher turns his back, the teacher can't see what the student wrote. Then the students scramble the number of that number into another number and calculate the difference between this number and the original number (decreasing large number). Then the teacher asked the students to cross out a non-zero number in the difference. At this time, the students read the remaining numbers out loud in any order. The teacher still turned his back on him, but he could tell what the crossed-out number was.

The trick of this magic is obvious. The difference between these two numbers should be the root 9 of the number. When students cross out a number and read other numbers aloud, the teacher only needs to remove 9 from his mind and add other numbers. After the students finish reading, the teacher subtracts the last number from 9, and the result is the number that the students cross out (if the last number is 9, the students cross out 9).

The above magic and birthday mystery will greatly stimulate students' interest in learning simulation system.