How many quadruple digits can 123456 make up

How many quadruple digits can 123456 make up

6*5*4*3=360

Can we use 1, 2, 3, 4, 5 and 6 numbers to form a six digit number that has no repetition and can be divisible by 11? Why?

No, because the number divisible by 11 has the following characteristics: if the odd and even bit difference of a number is a multiple of 11 (or 0), then the number can be divisible by 11, otherwise it can't. That is, add the number on odd bit and the number on even bit from the right to the left, and then calculate their difference. If the difference is a multiple of 11 (including 0), then it turns out that First of all, the difference can't be 0, because if it is 0, the sum of odd bits and even bits are equal, so the sum of all numbers of this number must be even, but 1 + 2 + 3 + 4 + 5 + 6 = 21 is odd; second, the difference can't be 11, 22 and other non-zero times of 11, because the sum of the largest three numbers 6, 4, 3 in 1, 2, 3, 4, 5, 6 is 13, while the sum of the other three numbers is 13 Therefore, we can't use 1, 2, 3, 4, 5, 6 numbers to form a six digit number that can be divided by 11 without repetition

How many five digit numbers can be divided by 3 without repetition?
The answer to the exercise book is 216

Because 1 + 2 + 3 + 4 + 5 = 15 can be divisible by 3, there are only two cases: the five digits taken are 0, 1, 2, 4, 5 and 1, 2, 3, 4, 5. If the five digits taken are 0, 1, 2, 4, 5, then because 0 can not be in the first place, the five digit 4 × 4 × 3 × 2 × 1 = 9 without repeated digits can be formed