Aba
+bab
______
Ccc
All posible values for a b and c
start off with
121
212
-----
333
as long as there is no carry, things should work fine.
To find all possible values for a, b, and c in the equation "Aba + bab = Ccc," we need to analyze the patterns and restrictions.
Let's break it down step by step:
1. A + b = C:
From the leftmost column, we can see that A + b should be equal to C; otherwise, the equation would not balance. Since A and C are capital letters, they represent digits from 0 to 9, and b represents a digit from 1 to 9 (as adding 0 would not change the result).
2. a + a = c:
From the second column, we see that a + a should equal c. Since a and c are lowercase letters, they also represent digits from 0 to 9. However, since c is the sum of two identical digits, it can only be an even number. Therefore, a must be an even digit (0, 2, 4, 6, or 8).
Taking both conditions into account, we can list the possible combinations:
A = 1, b = 9, C = 0, a = 0, c = 0
A = 2, b = 8, C = 1, a = 0, c = 1
A = 3, b = 7, C = 2, a = 2, c = 4
A = 4, b = 6, C = 3, a = 2, c = 4
A = 5, b = 5, C = 4, a = 4, c = 8
A = 6, b = 4, C = 5, a = 4, c = 8
A = 7, b = 3, C = 6, a = 6, c = 2
A = 8, b = 2, C = 7, a = 6, c = 2
A = 9, b = 1, C = 8, a = 8, c = 6
These are all the possible combinations of values for a, b, and c that satisfy the given equation.