Calculus

In the multiplication shown below, the digits have been replaced by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

1. 👍 0
2. 👎 0
3. 👁 78
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.

1. 👍 0
2. 👎 0
posted by drwls
2. ABCDE 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).

1. 👍 0
2. 👎 0

Similar Questions

1. Calculus

In the multiplication shown below, the digits have been replaced by letters: different letters represent different digits, and the same letters represent the same digits.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 ======

asked by Nick on December 10, 2007
2. math

License plates consist of letters and/ or digits. Calculate the number of licence plates that could be formed in each province or territory. Assume all numbers and letters are possible. a) Ontario, with 4 letters followed by 3

asked by Kim on July 9, 2017
3. maths

In the equation (he)^2 = she the letters represent digits.Find replacements for the letters to make the statement true.

asked by Noah Sithole on July 16, 2014
4. discrete math

Q: Count the number of passwords with following constraints. Assuming digits = {0, 1, …..9}, letters = {a, b, ….. y, z} (a) 5 characters which are digits or letters. (b) 4 characters which are digits or letters, with at least

asked by akash on April 30, 2017
5. discrete math

Q: Count the number of passwords with following constraints. Assuming digits = {0, 1, …..9}, letters = {a, b, ….. y, z} (a) 5 characters which are digits or letters. (b) 4 characters which are digits or letters, with at least

asked by akash on May 1, 2017
6. Pre

How many different license plate number can be made using 2 letters followed by 4 digits selected from the digits 0-9 a) if letters and digits may be repeated? b) if letters may be repeated, but digits may not be repeated? c) if

asked by Kelley on April 29, 2017
7. math

in roman numerals, letters represent numbers. for example, I=1,V=5,X=10,L=50,C=100. letters in roman numerals are written next to each other; this is how the value of the number is shown. to read the numbers below, add the values

asked by shion on August 27, 2012
8. Computers

In Python - A state creates license plates, each containing two letters followed by three digits. The first letter must be a vowel (A,E,I,O,U), and duplicate letters and digits are allowed. The second letter can be any letter of

asked by Sheryl on April 22, 2013
9. Math110

how many 6 - slots codes can be made up using 2 letters followed by 2 digits followed by 2 letters where All of the following conditions must be met: a. the allowable letters are A through G b. the allowable digits are 2 through 7

asked by Demon on April 1, 2013