Question

Please help!!!!!!!!
If you multiply the four-digit number abcd by 4, the order of digits will be reversed. That is , abcd x 4=dcba. The digits a, b,c and d are all different. Find abcd. That means what numbers are abcd equal to?

Answer 1

i dunderstand

Answer 2

First, a has to be either 1 or 2, as if it's 3, then we'll get a number at least 12,000.

Answer 3

a must be 2, since 4 times any number will never equal 1... so

Answer 4

d has to be 8 or 3, since 4*8=32 and 4*3 = 12, there's no other number that'll give a 2 where a is.

Answer 5

I used trial and error to work out the answer
Using @agent0smith 's logic of the first number being '2'

I simply substituted numbers in from 1-9 to try and establish a number that satisfied the conditions

I get the number to be 2178*4=8712

Maybe ^^ can explain a more mathematical method that doesn't take ages!

Answer 6

And... d can't be 3, since the number is at least 2000 since a=2... 4*2000 must be at least 8000, so d is 8.

Answer 7

From there it might just be easier to do trial and error... the only available numbers are
1, 3, 4, 5, 6, 7, 9