A $10$ digit number with distinct digits is given and using all of its digits two new numbers are created. The sum of the two new numbers is $99999$ and their product is the same as the $10$ digit number.
Our aim is to find the number.
$\underline{\text{My Observations:}}$
Note that since the sum of the two new numbers is $99999$, we can pair two digits in the following way for their sum to be 9: $$0+9,1+8,2+7,3+6,4+5$$ The new numbers created must consist of 5 digits.