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Sum, Times, I Wonder.. (Posted on 2003-10-24) Difficulty: 3 of 5
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?

See The Solution Submitted by DJ    
Rating: 4.4286 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: First Thoughts... | Comment 3 of 7 |
(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

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