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Letter Calculations is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

If you take the problem 11x11=121, and replace the 1s with As and the 2s with Bs, you get AAxAA=ABA.

Using that same replacement idea, you can also generate AAxAA=BBCC. New values may or may not have been assigned to each letter.

Can you figure out what A, B and C equal in the above equation?

UK Version

If you take the problem 11 x 11 = 121 and replace the 1s with As and the 2s with Bs, you get AA x AA = ABA.

A similarly-generated letter equation would be AA x AA = BBCC. Can you work out what A, B and C equal in the above equation? The values of A and B may or may not have changed from the first example.

Hints




Click a Tab to reveal the Hint.

US Version

Each letter is represented by a single-digit number, so the possibilities for what number represents each letter are fairly limited.

UK Version

Each letter is represented by a single-digit, so the possibilities for each letter represents are fairly limited.

US Version

If you start by subbing in 1 for A and work your way through all the other numerical possibilities for A, you'll find your answer before long. What's more, if you use a calculator, trying out every possibility will take only a minute or two.

But if you can, try to solve it just using your head.

UK Version

If you start by replacing A with 1 and work your way through all the other possible digits for A, you'll find your answer before long. What's more, if you use a calculator, trying out every possibility will take only a minute or two.

But if you can, try to solve it just using your head.

US Version

As detailed in Hint Two, if you substitute every digit for A and work your way up, you'll find the answer in the last half of your search.

UK Version

Try substituting each digit for A and working your way up, as detailed in Hint 2. You'll find the answer in the last half of your search.


Solution

Incorrect

Too bad!

US Version

Try walking through your calculations one more time.

UK Version

Try running through your calculations one more time.

Correct

Sharp thinking!

US Version

88x88=7744

The numbers work out perfectly if you assign A a value of 8, B a value of 7, and C a value of 4.

At first, the possibilities for what goes where may have seemed daunting, but once you realize that only a few numbers can potentially replace A, everything starts coming together.

UK Version

88 x 88 = 7744

The numbers work out perfectly if you assign A a value of 8, B a value of 7 and C a value of 4.

This equation may seem daunting at first, but if you bear in mind that the potential values of A are limited, everything starts coming together

DB143S

A big thanks to http://professorlayton2walkthrough.blogspot.com

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