SIX + SEVEN + SEVEN = TWENTY
This is a standard alphametic, no hidden rules.
(An alphametic is a puzzle in which every letter corresponds to exactly one number, and only one letter can correspond to one specific number. The goal of the puzzle is to find the numbers for each letter.)
Please provide an explanation/reasoning and don't use brute force as reasoning. Brute force is still allowed, only to support the reasoning.
Edit: A few additional puzzles.
ONE + NINE + TWENTY + FIFTY = EIGHTY
TEN + TEN + FORTY = SIXTY