All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information