# Calculus

posted by .

In the multiplication shown below, the digits have been replaced by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

• Calculus -

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 -

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).

## 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In the multiplication shown below, the digits have been replaced by letters: different letters represent different digits, and the same letters represent the same digits.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?
2. ### math

If 3 different digits represent 3 different letters and each time a letter appears it represents the same digit how do i find the sum of the 3 digits represented?
3. ### math

Each time the same letter appears it represents the same digit.Different letters represent different digits.C+C=D;D+E=17;A+2C=D;2B+C=8.Find the sum A+B+C+D+E
4. ### 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 the …

In the multiplication problem at the right different letters stand for different digits, and ABC and DBC each represent a three digit number. What number does DBC represent?
6. ### Maths

Looks uses different letters to represent different digits and writes numbers using those digits.she notes that the successor of a number ABB is XYY and the predecessor of AYY is BB.can you find the value of A+B+X+Y
7. ### 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?
8. ### 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 1 …
9. ### 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 1 …
10. ### 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 digits …

More Similar Questions