ABCDEx4 = EDCBA. HELP MATH PROS?

Question

It seems that I can't solve this problem. I don't know how to start...
ABCDE
x 4
EDCBA

WTF????

Answer 1

A cannot be > 3. A cannot be 1 because if it were 1, then E could not be defined. Try putting a number from 0-9 in E when A is 1. You will find that 4 times 0-9 will not give you a number A = 1, obviously assuming that applies in the ones digit. So A = 2, and if A = 2, then E is either 3 or 8 but it is 8 because 2BCDE x 4 = 8DCBA. Now we know that the number is 2BCD8 x 4 = 8DCB2.

Now focus on the letter B. If B is multiplied by 4, B CANNOT be greater than or equal 3. Why? Because that would force a carriage of a 1 on top of A and it would cause E to be to be 9, but we said E = 8. So, B = 1 or 2. Let us assume B = 2. We know that 4D + 3 = B (in ones digit). Now go for it. Plug numbers from (0-9) in D in that equation and see if you get a 2 in the ones digit.
4D + 3 = B (ones digit)
D=1, B=7
D=2, B=1
D=3, B=5
D=4, B=9
D=5, B=3
D=6, B=7
D=7, B=1
D=8, B=5
D=9, B=9
B is not 2; B can’t be greater than 3. B=1.
21CD8 x 4 = 8DC21

.......1 3
2 1 C 2 8
X 4
8 2 C 1 2

To find D, look at the equation 4D + 3 = 1.
From previous table you can see that D = 2 or 7.
Assume D = 2, you will see there is no value for C if D=2.
So D = 7.

....3 3 3
2 1 C 7 8
X4
8 7 C 1 2
Now for sure there must be a 3 on top of 1. If C > 7, you will get that 3 on top of 1.
C = 7, 8, or 9. C = 9 would make the complete statement true.
ABCDE = 21978. Good game.

hey btw, this problem may be for PROS, but it's really not MATH. so your question should say HELP PROS

Answer 2

21978
x 4
---------
87912

A must be 1 or 2, or else the product will be 6 digits long.
But A must also be even, since E*4 ends in A.
So A is 2.

Then E must be 3 or 8, since E*4 ends in 2, but E must be at least 4, since A*4 (plus any carry over) equals E, so E is 8.

Therefore there is no carry over after B*4, so B must be 0, 1, or 2. But D*4 plus 3 (carry over) ends in B, so B must be odd, thus B is 1.

Since D*4 + 3 ends in 1, D must be 2 or 7. But if D=2 then C*4 + 1 ends in C. This is not possible, so D=7.

The only digit left is C, and by trial and error of the remaining possibilities only C=9 works.

Answer 3

this isn't mathematically true. unless one or all of them equal zero.
multiplication is communitive so switching the order meaningless. so AB=BA. this means that ABCDE=EDCBA. if you replace this string of varibles with one varible x. you get
x X 4 = x. the only thing that would make this true is if x =0 therefore ABCDE= 0. which means that one or all of the varibles equals zero. I hope that makes some sense to ya.

Answer 4

ABCDE x 4 EDCBA = paris hilton

Answer 5

ABCDE
x4
EDCBA

A = 2
B = 1
C = 9
D = 7
E = 8

21978
x4
87912