There are nine cards of 0, 0, 0, 1, 1, 1, 2, 2, 2.
When taking four cards out of these cards and making the integer of 4 figures, how many kinds of integer can be made in all?
How many numbers of integers become multiple of 3?
Noted that 0001, 0122, etc. are not counted as the integers of 4 figures.
Answer
52 kinds，
18 kinds
Solution
Supposing there are four cards of 1 and 2, 2 × 3 × 3 × 3 = 54 kinds integer will be made in all.
However, since there are only three cards of 1 and 2, 1111 and 2222 cannot be made.
Therefore, 54 - 2 = 52 kinds.
When the sum of each digit number of a certain figure would become a multiple of 3, it becomes a multiple of 3.
Three kinds of integers are made with four figures of 0, 1, 1, 1.
Six kinds with 0,0,1,2, three kinds with 0,2,2,2 ans six kinds with 1,1,2,2 can be made.
Above all, there are 3 + 6 + 3 + 6 = 18 kinds.
When taking four cards out of these cards and making the integer of 4 figures, how many kinds of integer can be made in all?
How many numbers of integers become multiple of 3?
Noted that 0001, 0122, etc. are not counted as the integers of 4 figures.
Answer
52 kinds，
18 kinds
Solution
Supposing there are four cards of 1 and 2, 2 × 3 × 3 × 3 = 54 kinds integer will be made in all.
However, since there are only three cards of 1 and 2, 1111 and 2222 cannot be made.
Therefore, 54 - 2 = 52 kinds.
When the sum of each digit number of a certain figure would become a multiple of 3, it becomes a multiple of 3.
Three kinds of integers are made with four figures of 0, 1, 1, 1.
Six kinds with 0,0,1,2, three kinds with 0,2,2,2 ans six kinds with 1,1,2,2 can be made.
Above all, there are 3 + 6 + 3 + 6 = 18 kinds.
