##
Nine Digits Sum

ABC+DEF=GHI. Replace each letter with a unique digit from 1 to 9, such that
GHI is
- as small as possible.
- as large as possible.

Repeat for ABC+DEF=GHIJ, using the digits 0 to 9, with no leading zeros.
To avoid duplication in answers, maximize DEF in each solution.
I'm interested more in analytical proofs than in computer generated solutions.

Source: Original. Based on a puzzle from The 2001 Mensa Puzzle Calendar.

Solution

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