□+□□+□□□+□□□□
You are given that the numbers 0,1,2,…,9 are to be filled in the square boxes as shown above (without repetition) such that it represent a sum of a 1-digit, 2-digit, 3-digit, and 4-digit number.
Find total number of possible arrangements of these nine numbers such that the sum of these four numbers is minimized.
Details and Assumptions:
- This is an arithmetic puzzle, where 1□ would represent the 2-digit number 19 if □=9. It does not represent the algebraic expression 1×□.
- The numbers are not allowed to have a leading 0 (even the 1-digit number).
- See Part 1, Part 2 and Part 4.