There are infinitely many pairs of numbers whose sum equals their product.

However, there is only one solution to the equation below, in which each letter stands for a single, distinct digit.

AB × C.DE = AB + C.DE

What digit does each letter in this equation represent?

(In reply to First Thoughts... by SilverKnight)

Much faster: if ABxC.DE=AB+C.DE, subtracting C.DE from both sides and reordering terms, we get C.DE=AB/(AB-1).

Since AB and (AB-1) are relatively prime to each other, 1/(AB-1) must be a non-repeating fraction, so AB-1 must divide 100, which allows just a few values.

Running through those values, AB=26 solves the problem.

Posted by Federico Kereki on 2003-10-24 11:53:23