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

Home > Numbers
Either way (Posted on 2022-01-05) Difficulty: 3 of 5
Consider a pair of 3-digit numbers 122 & 213.
Their product is 25986.
Invert both numbers and consider the new product- it is 68952 i.e. inversion of the previous result!

List all such pairs of 3 digit numbers, avoiding trivial solutions.

Are there such pairs of 4 digit numbers?

Either find some or prove there are none.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Part 2 (spoiler) | Comment 1 of 8
Any pair of numbers that avoids carries when adding the partial products will do.

For instance, 1112*2113 = 2349656
                    2111*3112 = 6569432

Note the lack of carries:
           1112
        X 2113
           3336
1112
1112
2224
        2349656     
 Extra credit:

Here are some of the non-trivial 7 digit numbers that work
1111112 X 1111121 = 1234579876552
2111111 x 1211111 = 2556789754321

              

  Posted by Steve Herman on 2022-01-05 07:58:24
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information