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Wonderful 19 digits
Can be determined in turn:
According to the property that the left number can be divisible by 5,0,5, 10+05.
According to the divisibility of 2 x, the multiple of 4 is 2/6, other even numbers are 4/8, and other odd numbers are 1/3/7/9.
According to the divisibility of 9, the digit of 19 is 9 (the sum of the preceding digits of 18 should be a multiple of 9).
At this point, there are only 22,680 possible states left, and the computer will soon exhaust them. ...
The sum of the first 9 digits is a multiple of 9.
The difference between the first 1 1 bit and the sum of odd and even numbers is a multiple of 1 1.
In this 1 1 digit, the sum of six odd numbers is even.
The maximum of 6 odd numbers is 5/9/7/7/3/3 and 34; The minimum values are 5/11/3/3/7 and 20.
4 Even numbers up to 8/8/6/6,28; The minimum values are 2/2/4/4 and 12.
The range of the sum is an even number of 32-62. After subtracting the odd bits 1 1, this sum is a multiple of 9 and can only be 45.
Because the sum of 456 bits is a multiple of 3, and the sum of 4 bits 2/6 and 6 bits 4/8 can only be 10.
Even if two bits take 8 and eight bits take 6, the sum of even bits is only 24, the sum of odd bits is 24, and 1 1 bit is 3.
After almost all the even numbers are determined, it is easy to determine the odd numbers of the first 9 bits according to the sum of every 3 bits divided by 3, but in fact such a set of solutions can not be found.
That is to say, when x reaches 1 1, it is impossible to satisfy that all the first x bits are divisible by x at the same time. Not to mention 13, 17, 19. .
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