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Difficult mathematical arrangements and combinations
Solution: Discuss according to the situation:

1, when D=3 and A+B+C=3, the sum of three numbers in 0~5 is 3 (regardless of the specific values of a, b and c), (0,0,3), (0, 1 2), (1. Assign these three values to A, B and C, and the total combination is: 1C3+3! +1= 3+6+1=10 (species)

Specific combination:

0033,0303,3003,0 123,02 13, 1023, 1203,20 13,2 103, 1 1 13

2. When D=2 and A+B+C=4, the sum of three numbers in 0~5 is 3 (without distinguishing the specific values of A, B and C), (0, 0, 4), (0, 1, 3), (0, 2, 2) and (655). Assign these four values to A, B and C, and the total number of combinations is 1C3+3! +1C3+1C3 = 3+6+3+3 =15 (species)

Specific combination:

0042,0402,4002,0 132,03 12, 1032, 1302,3 102,30 12,0222,2022,2202, 1 122, 12 12,2 1 12

3. When D= 1 and A+B+C=5, there are three cases: (0, 0, 5), (0, 1, 4) and (0, 2, 3), and the sum of three numbers in 0~5 is 3 (regardless of A, B and C). Assign these five values to A, B and C, and the total number of combinations is 1C3+3! +3! +1C3+1C3 = 3+6+6+3+3 = 21(species)

Specific combinations: 005 1, 050 1, 500 1, 0 1, 04 1, 10465438+ 023 1, 003.

4. When D=0 and A+B+C=6, the sum of three numbers in 0~5 is 3 (regardless of the specific values of A, B and C): (0, 1, 5), (0, 3, 3), (0, 2, 4), (65444). Assign these six values to a, b and c, and the total number of combinations is 3! + 1C3+3! + 1C3+3! +1= 6+3+6+3+6+1= 25 (species)

Specific combination:

0 150,05 10, 1050, 1500,50 10,5 100,0330,3030,3300,0240,0420,2040,2400,4020,4200, 1 140, 14 10, 4 1 10, 1230, 1320,2 130,23 10,3 120,32 10,2220

Synthesizing 1-4, we can see that a * * has10+15+21+25 = 71(species).

PS: Landlord, it took me a long time to write out the details one by one. If you don't adopt it, you will be sorry for me.

Hope to adopt. You can ask if you don't understand.