What is the answer to puzzle 145 in Professor Layton and the Diabolical Box?

This puzzle is also known as Letter Calculations. it is one of Layton's Challenges from The Tea Master's House. Hint 1: Each letter is represented by a single-digit number, so the possibilities for what number represents each letter are fairly limited. Hint 2: If you start by subbing in 1 for a and work your way through all the numerical possibilities for A, you'll find your answer before ions, trying out every possibility will take only a minute or two. But if you can try to solve it just using your head. Hint 3: As detailed in hint 2, if you substitute every digit for A and work your way up, you'll find the answer in the last half of your search. AA X AA = BBCC 88 X 88 = 7744 Solution: A equals 8, B equals 7, & C equals 4