The arithmetic mean of a set of nine different positive integers is 123456789. Each number in the set contains a different number of digits with the greatest value being a nine-digit number. Find the value of each of the nine numbers .
The only conceivable way there could be a unique answer is if all the numbers involved had some maximality/minimality conditions imposed on them (ias x+y=x-1+y+1, then any unqueness here must expliot some maximality of y or minimality of x; we have a maxmial number 999,999,999) . By inspection one sees that 123456789*9 can only be the sum of numbers satisfying your conditions if they are maximal wrt the constraints.
Also it's clear that 123456798
=1+11+111+1,111+.....111,111,111, which should give another hint