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?

additional possibilities   (to mention some):

(1 2 7), (3 4 5 6  8)   or

(1 2 4 7), (3 5 6  8)   or

(1 2), (3 4 5 6 7  8)   or

(1 3), (2 4 5 6 7  8)   or

(1 4), (2 3  5 6 7  8)   etc

 

The original question could be improved , like

"How many ways ...etc"

 

Posted by Ady TZIDON on 2013-01-30 06:22:21