ABCDEx4=EDCBA. Find the number valuesof each letter

This is a problem of cryptarithmetic where each letter represents a unique digit. The equation is ABCDEx4 = EDCBA.

Let's solve it step by step:

1. Since we are multiplying a five-digit number by 4, the result can be a five or six-digit number. But in our case, it's a five-digit number. So, the first digit must be 1 or 2. But A and E are the same, so A = E = 1 or 2.

2. If A = E = 1, then B must be 2, 3, or 4. But B and D are the same, so B = D = 2, 3, or 4. But if B = D = 2, then C must be 8 or 9. But C and C are the same, so C = 8 or 9. But if C = 8, then E must be 3. But A = E = 1, so this is impossible. So, C = 9. But if C = 9, then E must be 6. But A = E = 1, so this is impossible. So, A = E = 2.

3. If A = E = 2, then B must be 3, 4, or 5. But B and D are the same, so B = D = 3, 4, or 5. But if B = D = 3, then C must be 2. But C and C are the same, so C = 2. But if C = 2, then E must be 8. But A = E = 2, so this is impossible. So, B = D = 4.

4. If B = D = 4, then C must be 6 or 7. But C and C are the same, so C = 6 or 7. But if C = 6, then E must be 4. But A = E = 2, so this is impossible. So, C = 7.

5. If C = 7, then E must be 8. But A = E = 2, so this is impossible. So, there is no solution to this problem.

Please note that this is a logical approach to solve the problem and it might not be the only approach.