# Thread: Is there a solution?

1. ## Is there a solution?

A three-digit number 'xyz' is such that the number equals x!+y!+z!.Find the difference of the number formed by reversing its digits and the original.

2. Interesting problem

145 does the trick.

$1!=1$
$4!=24$
$5!=120$
$1!+4!+5!=145$

if you just look 7! is more that 3 digits, so none of the numbers can be 7.
$6!=720$ which means the number would have to have at least a 7 in the first place, which means it is too big by above.

This narrows your choices to 1,2,3,4,5.
If you use all 4 or lower its not enough to get up into the 3 digits.

So you know there has to be a 5 in there somewhere. From there I just played around with it.