The five-digit number 31d26

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is divisible by 3. Find the sum of
all possible values of d.

d must be divisible by 3, it must be 0,3,6,9 the sum is 18

I would insert values 0-9 and divide by three, adding those numbers that give whole number answers.

31026/3 = 10342 (That's one.)

To determine if a number is divisible by 3, you need to find the sum of its digits and check if the sum is divisible by 3.

In this case, the number is 31d26, and we need to find the possible values of d such that the number is divisible by 3.

To find the sum of the digits of 31d26, we add the digits together: 3 + 1 + d + 2 + 6 = 12 + d.

Now we need to find the values of d that make the sum divisible by 3.

For the sum to be divisible by 3, the sum itself must be divisible by 3. Therefore, we need to find the possible values of d that make (12 + d) divisible by 3.

Let's check these possible values of d:

1. If d = 0, then the sum becomes 12 + 0 = 12, which is divisible by 3.
2. If d = 1, then the sum becomes 12 + 1 = 13, which is not divisible by 3.
3. If d = 2, then the sum becomes 12 + 2 = 14, which is not divisible by 3.
4. If d = 3, then the sum becomes 12 + 3 = 15, which is divisible by 3.
5. If d = 4, then the sum becomes 12 + 4 = 16, which is not divisible by 3.
6. If d = 5, then the sum becomes 12 + 5 = 17, which is not divisible by 3.
7. If d = 6, then the sum becomes 12 + 6 = 18, which is divisible by 3.
8. If d = 7, then the sum becomes 12 + 7 = 19, which is not divisible by 3.
9. If d = 8, then the sum becomes 12 + 8 = 20, which is not divisible by 3.
10. If d = 9, then the sum becomes 12 + 9 = 21, which is divisible by 3.

Therefore, the possible values of d that make 31d26 divisible by 3 are 0, 3, 6, and 9.

To find the sum of all possible values of d, we simply add these values together: 0 + 3 + 6 + 9 = 18.

Hence, the sum of all possible values of d is 18.