Answer: See below
Explanation:
To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:
Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.
Then, the addition problem becomes:
A B C
D E F
We know that the sum of each column must be the same, so:
C + F = 10 + B
B + E = 10 + A
We can rewrite these equations as:
C - B + F = 10
B - A + E = 10
Since we are given that the sum of the two numbers is the same, we know that:
C + F + D + E = 1112
We can substitute C and F in terms of A and B using the equations above:
C = 10 + B - F
F = 10 + C - B
Substituting these expressions into the equation for the sum, we get:
10 + B - F + C + D + E = 1112
Simplifying this equation, we get:
B - F + C + D + E = 1102
Now we can substitute in the expressions for C and F in terms of A and B:
B - (10 + B - F) + (10 + C - B) + D + E = 1102
Simplifying and canceling out terms, we get:
F - C - D - E = -92
We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.
Trying different values for A and D, we find that A = 2 and D = 3 works:
A B C
D E F
2 7 9
1 7 3
The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:
2 7 9
1 7 3
4 5 2