Find the 9 Values of a Set of Positive Integers

[PrudensOptimus]

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 .

 

[Moose352]

9,99,999,9999,99999,999999,9999999,99999999,999999999

 

[PrudensOptimus]

how?

 

[matt grime]

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

 

[Moose352]

I immediately recognized that 123456789 = 1+11+111+1111...111111111, like Grime said. Knowing this, multiply both sides by 9, and find the answer.

Also like Grime said, the values must be that maximums, which means that there is only one correct answer.