Sphinx's Riddle

Logic Level 3

You are facing the Sphinx guarding the exit portal of the pyramid. On the stone wall, there are 9 stone tablets arranged in \(3\times3\) square with inscribed runes you can't read (but we designate them as \(A\) to \(I\) for simplicity as shown), and behind each tablet is a distinct digit from 1 to 9.

The Sphinx then asks you to answer all the hidden numbers correctly without flipping any tablet, or you'll be eaten alive, before giving you 3 clues:

Clue #1: The sum of three numbers in each row, column, and diagonal involving the center equals to 12.

Clue #2: The product of three numbers in each row and column not involving the center is over 107.

Clue #3: The number in the upper left corner (\(A\)) can divide the number in the lower left corner (\(G\)).

What is the value of 9-digit integer \(\overline{ABCDEFGHI}\)?


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