# in the addition problems below each leter represents the same digit in

both problems. Replace each letter with a different digi, 1-9, so that both addition problems are true.(there are two possible answers.)
A B C A D G
+D E F +B E H
------ ------
G H I C F I

## To solve this problem, we need to find values for each letter (A, B, C, D, E, F, G, H, I) such that both equations are true when digits are substituted for the letters. Let's break it down step by step.

Since each letter represents a different digit from 1-9, we need to assign a unique digit to each letter. Let's start with the first equation:

A B C
+ D E F
--------
G H I

To simplify things, we can look at the rightmost column (units place):

C + F = I

The maximum values for C and F (when both are 9) would be 18. But since I is the units place digit, I should be between 0 to 9. This means C + F should be less than or equal to 9.

Now let's look at the middle column (tens place):

B + E + 1 = H + 10G

Since there is a carry (1) from the units place column, we add 1 to the sum of B and E. The maximum value for B + E (when both are 9) is 18. This means H + 10G should be greater than or equal to 19.

Finally, let's look at the leftmost column (hundreds place):

A + D + 1 = G

Again, there is a carry (1) from the middle column. The maximum value for A + D (when both are 9) is 18. This means G should be greater than or equal to 19.

Based on these conditions, we can start trying different combinations of digits for each letter and check if the equations hold true. We can create a program, use a spreadsheet, or solve it manually using trial and error.

Here is one possible solution:
A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9

1 2 3
+ 4 5 6
--------
7 8 9

And here is another possible solution:
A = 1, B = 2, C = 4, D = 3, E = 6, F = 5, G = 7, H = 8, I = 9

1 2 4
+ 3 6 5
--------
7 8 9

Therefore, there are two possible solutions for the given addition problems.