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

Home > General
Group Endeavor (Posted on 2013-01-29) Difficulty: 3 of 5
Consider Groups I and II consisting of positive integers from 1 to 7, where:
Group I = {1,2,4,7} and, Group II = {3,5,6}
It is observed that the sum of any two numbers of either group is either greater than the largest number or is in the other group.

For example, 1 and 2 belong to the first group whose sum (3) belongs to the second group. Also, 3 and 5 belong to the second group, whose sum (8) is greater than the largest number (6) in the second group.

Can you come up with arrangement of the first eight positive integers, that is from 1 to 8 inclusively, that satisfies the same two properties?

No Solution Yet Submitted by K Sengupta    
Rating: 1.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: POSSIBLE INTERPRETATION Comment 8 of 8 |
(In reply to POSSIBLE INTERPRETATION by Ady TZIDON)

Per your interpretation, the following partitions satisfy:

 1  2  3  4  5  6  7  8  |
 1  2  4  5  6  7  8  |  3
 1  2  4  6  7  8  |  3  5
 1  2  4  7  8  |  3  5  6
 1  2  4  7  |  3  5  6  8
 1  2  4  8  |  3  5  6  7
 1  2  4  |  3  5  6  7  8
 1  2  5  6  7  8  |  3  4
 1  2  5  7  8  |  3  4  6
 1  2  5  |  3  4  6  7  8
 1  2  6  7  8  |  3  4  5
 1  2  6  |  3  4  5  7  8
 1  2  7  8  |  3  4  5  6
 1  2  7  |  3  4  5  6  8
 1  2  |  3  4  5  6  7  8
 1  3  4  5  6  7  8  |  2
 1  3  5  6  7  8  |  2  4
 1  3  5  |  2  4  6  7  8
 1  3  6  7  8  |  2  4  5
 1  3  6  |  2  4  5  7  8
 1  3  |  2  4  5  6  7  8
 1  4  5  6  7  8  |  2  3
 1  4  |  2  3  5  6  7  8
 1  5  6  7  8  |  2  3  4
 1  5  |  2  3  4  6  7  8
 1  |  2  3  4  5  6  7  8

where the vertical bar separates the two sets. For brevity, the set with the 1 in it is shown only on the left; the two sets could be interchanged.

But in explaining the example, KS did say

"Also, 3 and 5 belong to the second group, whose sum (8) is greater than the largest number (6) in the second group."

specifying the same group.


  Posted by Charlie on 2013-01-30 13:33:59
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 (2)
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