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

Home > Numbers
Simultaneous Operations - Pairs (Posted on 2012-03-03) Difficulty: 3 of 5

No Solution Yet Submitted by brianjn    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solutions | Comment 2 of 4 |

For the sum, difference and product to be odd, odd and even, respectively, the smaller number must be odd and the larger one even (if the smaller one were even, so would be the larger).

The smallest larger number with each of the four smallest odd numbers is (with the eight numbers in the left two columns and their sum on the right):

   1   2   3
   3   6   9
   5  10  15 
   7  14  21  
         ---
          48  is the total of all 8 numbers.  

For task II, with sum, difference and product all even, both numbers must be even:

The smallest non-overlapping groups are:

   2   4   6
   6  12  18
   8  16  24  
  10  20  30  
         ---
          78
         

For part III, both numbers must be odd:
         
The smallest groups are:

   1   3   4  
   5  15  20
   7  21  28 
   9  27  36           
         ---
          88

  Posted by Charlie on 2012-03-03 15:12:55
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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information