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Math question: there is a number, divided by 7 over 2, divided by 8 over 4 and divided by 9 over 3. What is the minimum number? ?
This is the famous problem of Han Xin's ordering soldiers in the history of China, also known as the grandson problem.

The fixed solution is this:

solve

Find a number that is divisible by 7 and 8 and by 9 and 3. There is a fixed method:

56m-9n=3

Before calculating, you should make an appointment on both sides of the formula. There is no common factor at this time, so there is no need to make an appointment. )

The two coefficients 56 and 9, 56 are very large, so let 56 be divided by 9, and the quotient 6 is greater than 2, so

It can be simplified as (6*9+2)m-9n=3, 2m-9(n-6m)=3, let k=n-6m, and there are

2m-9k=3

The two coefficients 2 and 9, 9 is larger, 9 is divided by 2, and the quotient 4 is 1, so

It can also be simplified as 2m-(4 * 2+1) k = 3,2 (m-4k)-k = 3, and i=m-4k.

2i-k=3

There is a coefficient 1. When the coefficient is 1, we should leave a coefficient of 1, that is, 2 =1*1+instead of 2=2* 1+0.

i-j=3

At this time, the coefficients on both sides are 1, so it cannot be simplified, so j=0 and i=3.

Back, calculate k=j+i=3, m=i+4k= 15.

Let a=56m=280*3, then 7|a, 8|a, a is divided by 9 and 3.

In the same way, find:

B = 441* 4,7 | b, 9|b, b divided by 8 is greater than 4.

C=288*2, 8|c, 9|c, c divided by 7 and 2.

Then add up these three figures.

A+b+c=3 180。 Obviously, this number is divided by 7, 2, 4 and 3, but it is not necessarily the minimum.

The least common multiple of the numbers 7, 8 and 9 (with a fixed algorithm) is 7*8*9=504.

Then divide 3 180 by 504 and the quotient 6 is 156.

The result is 156.

PS: The above solution is a fixed algorithm, and any large number can be solved by this algorithm, without trying to guess. There is also a fixed algorithm for finding the least common multiple, that is, the greatest common divisor is obtained indirectly through division. 1, 30.

I knew it was wrong after typing it out, but unfortunately there was something wrong with the machine and it was not changed. , 2, 156, 1, there is a number, divided by 7 to leave 2, divided by 8 to leave 4, divided by 9 to leave 3, what is the minimum number?

2*288+4*44 1+3*280=3 180

The least common multiple of 7, 8 and 9 is: 504.

3 180/504=6。 . . . 156

At least:156,0, Math Problem:: There is a number, divided by 7 and remaining 2, divided by 8 and remaining 4, divided by 9 and remaining 3. What is the minimum number?

30 is wrong ... 156 is right, but I don't know if it is the smallest number ... how to calculate it and in what way? Is it convenient to communicate?

Where did 288 44 1 280 come from?