Prove that every integer greater than 1 has a multiple that is less than and can be written in the decimal system with at most four different digits.
%V0
Prove that every integer $k$ greater than 1 has a multiple that is less than $k^4$ and can be written in the decimal system with at most four different digits.
Source: Međunarodna matematička olimpijada, shortlist 1990
Školjka 
greater than 1 has a multiple that is less than 
and can be written in the decimal system with at most four different digits.