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 Group Endeavor (Posted on 2013-01-29)
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 |

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

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