Math Puzzle:

Leonhard correctly finishes a Sudoku puzzle, and tells you: "That's cool! When I look only at the upper left-hand 3 x 3 square of the puzzle, view each of the three-digit rows as a three-digit number, and add them together, I get 1000." Is he telling the truth?

An alternative version, if you prefer: You correctly tell Blaise, "I have three three-digit numbers that add up to 1001, and all the digits of all the numbers are different from each other." Right away, Blaise says, "You didn't use a 7 in any of them, right?" How did he know?

Tell me, please, which version you like better. Thanks to my father Vladimir for the Sudoku frame for the first problem. I thought up both problems yesterday, but I'm sure someone else has beaten me to them, maybe by centuries.