OT Math puzzle

OT
Favorite math puzzle.
Take a five digit number, multiply by four, get the same five digits (non-zero) in reverse order.
ABCDE x4 = EDCBA

Ron,
do you want another shot at this "favorite" or yours? Makes no sense.
Tom

12345 X 4 = 49380

didn't work work for me

ABCDE
x. 4
-----------
EDCBA

I think I missed something somewhere.

21978 x 4 = 87912

(quoted from post at 23:17:14 06/27/15) 21978 x 4 = 87912

Click to expand...

Sooooo.....is there a way to arrive at this answer, or just trial and error till you find one that works? I assume there must be a formula or something?

We're given a 5-digit number that becomes a new 5-digit number when multiplied by 4. Therefore
the first number can't be greater than 24,999 because 25,000*4 = 100,000. This means A has to
equal 1 or 2. "A" is also the last digit of the product, which has to be even if it's a
multiple of 4. Therefore A=2. Since A=2, B can't be more than 4, so it must be 1, 3, or 4.
Also, if "EDCBA" is a multiple of 4 then "BA" must be divisible by 4 too. Out of the
possibilities for "BA" (12, 32, 42), only the first two work. So B is 1 or 3.
Since A is 2 and B is greater than 0 but less than 4, then "ABCDE" is between 21000 and 24000.
This means EDCBA is between 84000 and 96000. So E is 8 or 9. But since A is 2, E*4 must end in
2. So E=8. Notice that 23,000 * 4 = 92,000. This means that ABCDE must be less than 23,000 if E
is to be 8. Thus B=1 and not 3.

Filling in the discovered values So far, we have: 21CD8 * 4 = 8DC12

If the product ends in "12", then 4D+3 must end in 1. (You can verify this by trying to
multiply 21CD8 * 4 by hand; 8*4=32, so you carry the 3, etc.) So D=2 or 7. If D=2, then using
the same reasoning, 4C+1 must end in the same digit as C. If D=7, then 4C+3 must end in the
same digit as C. This only works for D=2 C=3 and D=7 C=9. Out of these pairs, only the second
one gives positive results for ABCDE*4=EDCBA.

So the only solution is 21978*4=87912.

Google is my friend! LOL!

Greg you lost me with "We're given......" my head started to hurt right about then. LOL

I think he worded it wrong. He should have asked "what number can you multiple times 4 and the answer will be the same numbers in reverse order"

Mine is that 0 = 1. The guy in this video goes way out of his way to make it longer than it has to be, but if you follow him closely, he finally gets to 0 = 1.

Mark
0 equals 1

Bingo
If you enjoyed that, do it with 7 digits. or any number greater than 4.
The reason I enjoy it is that the arithmetic is easy ,but you must use everything you know about each number

Common core answer: purple. Because aliens don't wear pants.

Teacher, can I be excused? My brain is full.

My hard drive overloaded after the first digit. LOL Thank you for the interesting post nonetheless.