C: Find out 1 to 4000, the number of the number of the sum can be divisible by 4 how many?

Find out 1 to 4000, the number of numbers of the sum can be divisible by 4, such as: 745:7+4+5=16,16 can be divisible by 4, 28:2+8=10,10 not divisible by 4, 745 is such a special number, and 28 is not, ask: how many of these numbers?

Solution:

(1) For 4000,4+0+0+0=4, it is obvious that 4000 is the number satisfying the condition;

(2) for 1 to 3999, we treat each number as a 4-bit [][][][] form, the first digit [] takes 0 to 3, the latter 3 takes [0][0][0] to [9][9][9], and the sum of the 4-digit number is represented by sums:

2.1: If the latter 3 is an odd number, then the 1th place takes 1 or 3, must be able to make sum can be divisible by 4, such as sum=15,sum+1=16;sum=17,sum+3=20 can meet the conditions;

2.2: If the sum of the last 3 is an even number, may wish to use SUM1 to represent the sum of the last 3 digits, then divided into two situations, so that sum2=sum1/2, if sum2 is still even, then sum1 can be divisible by 4, the 1th position 0, can meet the conditions; if sum2 is odd, Then sum1 can not be divisible by 4, 1th position 2,sum=sum1+2 can meet the conditions;

So after 3 bit [0][0][0] to [9][9][9], always find a number in the 1th position, so that sum can be divisible by 4, because there is no number 0, so 1 to 3999 total 1000-1 = 999 numbers to meet the conditions;

In total, there are 999+1=1000 of such special figures.

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C: Find out 1 to 4000, the number of the number of the sum can be divisible by 4 how many?