What is the sum of all possible digits that could fill in the blank

in 47_021 so that the resulting five digit number is divisible by 3?

I have news for you. If I add a number to the blank, it makes six digits. My eyes are old and bad but not that bad (but still that old).

DrBob is right, you have a typo.

Nevertheless there is a nice quick way to check if any number is divisible by 3

Add up all the digits in the number, if that sum is divisible by 3 so was the original number.

so far the digits of 47_021 add up to 14, so you could add 1,4 or 7 and in each case the new number would be divisible by 3

To find the sum of all possible digits that could fill in the blank in 47_021 so that the resulting five-digit number is divisible by 3, we need to determine what properties a number should have in order to be divisible by 3.

A number is divisible by 3 if the sum of its digits is divisible by 3. Therefore, we need to find the digits that can be placed in the blank such that the sum of all the digits in the resulting five-digit number is divisible by 3.

Let's break this down step by step:

1. We start with the number 47_021. To make it divisible by 3, we need to find a digit to fill in the blank.

2. To determine the possible digits, we need to consider the digits that are left - the ones that haven't been used in the original number. The digits that are left are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

3. We now need to check if adding any of these remaining digits to the blank will make the sum of all the digits in the resulting number divisible by 3.

4. To do this, we need to consider the sum of the three known digits (4, 7, 0, and the digit that fills in the blank) and check if it is divisible by 3. We can calculate this sum for each possible digit.

For example, let's consider the case where the blank is filled with the digit 3. The number would then become 473021. To check if this number is divisible by 3, we need to calculate the sum of its digits: 4 + 7 + 3 + 0 + 2 + 1 = 17. Since 17 is not divisible by 3, we can conclude that filling the blank with the digit 3 does not make the resulting number divisible by 3.

5. We repeat this process for each possible digit that can fill in the blank (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and see which of them make the resulting sum divisible by 3.

6. Once we have checked all possible digits and found the ones that make the sum divisible by 3, we can calculate the sum of these digits.

To summarize, we need to calculate the sum of the digits that can be placed in the blank of 47_021 so that the resulting number is divisible by 3. This involves checking the possible digits and their respective sums with the original number.