In the multiplication shown below, the digits have been replaced by

letters: different letters represent different digits, and the
same letters represent the same digits. What was the origianl
multiplication?

ABCDE
x 4
======
EDCBA

please help tried it many times can't get it. It is drivin me nuts.

To solve this problem, we can use a technique called long multiplication, but with letters instead of digits. Let's break it down step by step:

Step 1: Write down the equation in the long multiplication format, where each letter represents a different digit:
ABCDE
x 4
======
EDCBA

Step 2: Start with the rightmost digit, which is 'E'. We need to multiply it by 4. Since 'E' is the same as the rightmost digit in the result 'EDCBA', we know that multiplying 'E' by 4 should give us a number that ends with 'E'. The only digit that works is 5. So, we can write:
ABCD5
x 4
======
EDCBA

Step 3: Next, we move to the second rightmost digit, which is 'D'. We need to multiply it by 4 and add the result to the next column: 'E'. Since 'D' is the same as the second-rightmost digit in the result 'EDCBA', we know that multiplying 'D' by 4 should give us a number that ends with 'D'. The only digit that works is 6. So, we can write:
ABC65
x 4
======
EDCBA

Step 4: Continuing this process for 'C', 'B', and 'A', we find that the values for these letters are 7, 8, and 9, respectively. So, we can complete the multiplication as follows:
ABCDE
x 4
======
EDCBA

97865
x 4
======
89176

Therefore, the original multiplication was 97865 multiplied by 4, resulting in 89176.