What 4 digit number dcba equals abcd multiplied by 9?

Answer 1

Well, honey, if you want to find a 4-digit number where the digits are reversed when multiplied by 9, the number you're looking for is 1089. That's the only number that plays nice and keeps its digits in line when you multiply it by 9. So, there you have it - 1089 is the magic number you're after.

Answer 2

dcba = 9 x abcd

dcba/9 = abcd

Since the quotient is also a 4 digit number, then d in order to be divided by 9, must be the biggest digit which is 9. So that d = 9 and a = 1. The same way for other digits...

So that we have:

dcba = 9 x abcd

9999 = 9 x 1111