Box Progression Part 3

Logic Level 3

+++ \large \square + \square\square+\square\square\square+\square\square\square\square

You are given that the numbers 0,1,2,,90,1,2,\ldots,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 1 \square would represent the 2-digit number 19 if =9 \square = 9 . It does not represent the algebraic expression 1× 1 \times \square .
  • The numbers are not allowed to have a leading 0 (even the 1-digit number).
  • See Part 1, Part 2 and Part 4.
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