Friday

April 18, 2014

April 18, 2014

Posted by **Nick** on Wednesday, December 12, 2007 at 8:17pm.

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.

- Calculus -
**drwls**, Wednesday, December 12, 2007 at 11:15pmSomeone recently asked and someone else answered the similar question

ABCD x 4 = DCBA

In that case there was only one answer. It took quite a bit of reasoning to come up with the answer, 2178 x 4 = 8712

In your case, it is likely that there is no answer. The longer the string of numbers, the less likely it is that there is an answer. The problem has to be done by a "cut and try" method. If you try to do it with algebra, you end up with one equation and 4 unknowns.

- Calculus -
**Count Iblis**, Thursday, December 13, 2007 at 10:02amABCDE x 4 = EDCBA

21978 x 4 = 87912

You just use the fact that the last digit of a multiple of 4 is even. It is not zero, because A = 0 would mean that the number ABCDE is actually a four digit number. It cannot exceed two otherwise you get a six digit number when multiplying it by four. So:

A = 2

This means that the number will be EDCBA will be larger than 80,000 so E has to be 8 or 9. But E = 9 as the first digit of ABCDE

yields A = 6, so E must be 8. You then simply work your way through the multiplication. It is straightforward to come up with the answer (i.e., if it exists as in this case).

**Related Questions**

Calculus - In the multiplication shown below, the digits have been replaced by ...

math - If 3 different digits represent 3 different letters and each time a ...

math - Each time the same letter appears it represents the same digit.Different ...

Math - A state creates license plates that each contain two letters followed by ...

Math - A state creates license plates that each contain two letters followed by ...

statistics - . License plates are made using 2 letters followed by 3 digits. How...

math - Suppose a license plate requires three letters ,followed by three digits....

statistics - Basic Concepts of Probability and Counting 1. License plates are ...

Math - A password consists of 2 letters and 2 digits (0-9). The letters and ...

Computers - In Python - A state creates license plates, each containing two ...