All,
A magic square is an NxN square filled with distinct integers where all columns, rows and diagonals add up to the same value. Here is an example 3x3: 
4 3 8
9 5 1
2 7 6

[download]

What I am trying to create has similar properties (all selections add up to the same value). A selection is defined where N numbers are chosen from the square such that each column and row may only have 1 number selected from it. Here are the possible choices for a 3x3. 

SQUARE

A B C
D E F
G H I

SELECTIONS (order is not important)
A E I
A H F
D B I
D H C
G B F
G E C

[download]

This would be trivial if there wasn't a requirement for distinct values (making all values 1 for instance would suffice). Making a 2x2 is also trivial. 

3 9
1 7

3 + 7 = 10
1 + 9 = 10

[download]

Ultimately, I would like squares for N=3, N=4, N=5 and possibly N=6. It doesn't matter what sum the selections add up to provided that each value is a distinct integer. Can you do it?

Cheers - L~R

In reply to Not A Magic Square But Similar by Limbic~Region

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