What is the sum of the six three-digit numbers that have the digits 1, 2, and 3? What is the sum in each column? Why is the sum in each column the same? my mom doesn't know how to help me with this one?
Each column will have 2 1's, 2 2's, and 2 3's.
So, each columns will total to 12.
so, adding in the carries between columns,
12 12 12 makes 1332
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To find the sum of the six three-digit numbers that have the digits 1, 2, and 3, we'll need to find the possible arrangements of these digits.
The given digits are 1, 2, and 3. We can start by fixing the first digit, which can be any one of the three digits. Let's consider the cases for each fixed first digit:
1. If the first digit is 1:
- The second digit can be either 2 or 3.
- The third digit can be the remaining digit (i.e., if the second digit is 2, then the third digit is 3, and vice versa).
- The possible three-digit numbers are: 123 and 132.
2. If the first digit is 2:
- The second digit can be either 1 or 3.
- The third digit can be the remaining digit (i.e., if the second digit is 1, then the third digit is 3, and vice versa).
- The possible three-digit numbers are: 213 and 231.
3. If the first digit is 3:
- The second digit can be either 1 or 2.
- The third digit can be the remaining digit (i.e., if the second digit is 1, then the third digit is 2, and vice versa).
- The possible three-digit numbers are: 312 and 321.
Now, let's calculate the sum of these six three-digit numbers:
123 + 132 + 213 + 231 + 312 + 321 = 1,332.
To find the sum in each column, we can add the digits vertically. Here's how:
1 2 3
+ 1 3 2
+ 2 1 3
+ 2 3 1
+ 3 1 2
+ 3 2 1
-----------
9 12 12
Starting from the ones column, we find that the sum is 9. Moving to the tens column, we can see that the sum is 12. Finally, in the hundreds column, the sum is also 12.
The sum in each column is the same because each column represents the same place value (ones, tens, and hundreds) for all the numbers being added. Therefore, the sum in each column must be equal.