Box Progression Part 4

Logic Level 2

\[ \large \square + \square\square+\square\square\square+\square\square\square\square \]

You are given that the numbers \(0,1,2,\ldots,9\) 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 ten numbers such that the sum of these four numbers is maximized.

Details and Assumptions:

  • For the purposes of this question, 0 is considered a 1-digit number.
  • This is an arithmetic puzzle, where \( 1 \square \) would represent the 2-digit number 19 if \( \square = 9 \). It does not represent the algebraic expression \( 1 \times \square \).

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