Question 47
Find the natural numbers $x\lt y\lt z$ whose sum is $2021$ and which simultaneously satisfy the following conditions:
- **(a)** The digits within each number are all distinct.
- **(b)** There exist three distinct digits $a,b,c$ such that every digit occurring in $x,y,z$ is one of $a,b,c$.
- **(a)** The digits within each number are all distinct.
- **(b)** There exist three distinct digits $a,b,c$ such that every digit occurring in $x,y,z$ is one of $a,b,c$.