AB+B=BA is a puzzle in Professor Layton and the Diabolical Box.


Let's replace the numbers in the equation 12+12=24. A is now one, B is now two, and C is now four, which gives up the new equations AB+AB=BC.

Now think about another such equation, AB+B=BA, where the letters may have different values from the sample equation above.

What numbers could replace the A and the B to make this second equation true? Keep in mind that A and B are different numbers.


Click a Tab to reveal the Hint.

If you added B and B together, the digit in the ones place (the last digit) of the resulting sum would equal A.
Since no two single digit numbers can add up to more than 18, you know the number in the tens place of the sum of B+B must be one. The only other value that influences the tens place in the solution is the A in AB+B.
Therefore, A+1 must equal B.



Great job!

If you replace the A with an eight and the B with a nine, then the equation is true because 89+9=98.


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