SOLUTION: Two numbers are mirror numbers if one can be obtained from the other by reversing the order of the digits. Find two mirror numbers whose product is 92565.

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Question 1113547: Two numbers are mirror numbers if one can be obtained from the other by reversing the order of the digits. Find two mirror numbers whose product is 92565.
Found 2 solutions by greenestamps, josmiceli:
Answer by greenestamps(13200) (Show Source):
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(1) The two numbers have to be 3-digit numbers.
(2) The product ends in 5, so one of the numbers ends in 5 and the other begins with 5: 5AB*BA5 = 92565.
(3) The product is 5AB*BA5 = 92565; from that we can conclude that B is 1 (any larger value for B would make the product 6 digits): 5A1*1A5 = 92565.
(4) Now the product is 5A1 * 1A5 = 92565; from that we can conclude that A is a "large" digit. A can't be 7, because 571*175 would be divisible by 25, and the product is not divisible by 25. And rough estimation shows A=8 is too big for the given product. So try A=6 and it works: 561*165 = 92565.

A purely algebraic solution would be a nightmare; even an algebraic solution after we get to the point where we know the product is 5A1*1A5 is awkward.

The above solution using logical reasoning and a bit of trial and error seems the easiest path to the answer.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
In order to have a in the units
digit, at least one of the units digits
of the numbers must be
Also, the two number must be 3-digit numbers
since ( much too high )
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So, the two numbers look like
and
The products are:

I know that can't be , since that would
make the product greater than , so

I just tried whole numbers on this

So the numbers are and
( check it )