**Magic 7-Square and 2-Negative**

Regarding the enigma that asks for a 3x3 magic square
with 7 square entries, how to deal with the 2 non-square entries if they
are negative?

For example, any 3x3 magic square can be put into the
following form with a and b positive. Note that c-a-b is the smallest entry
and if a + b > c, the smallest entry will be negative.

c+a c-a-b c+b

c-a+b
c c-b+a

c-b c+a+b c-a

Suppose that the following 7-square solution was found with the smallest entry negative. Note that this configuration is similar to the one known 7-square solution.

d^2 -E f^2

g^2
h^2 i^2

j^2 k^2 L

Is it possible to rearrange the square entries so that the
non-squares are both positive?

Is it possible to modify the values and get
another 7-square solution with all entries positive?

I don't see how in this
configuration.

==============

In some configurations, it is possible to rearrange the square
entries so that the non-square entries have different values and become positive.

For
example, this can be done with a tilted magic hourglass because both the smallest
and largest entries are non-squares.

d^2 -E f^2

g^2 h^2
i^2

j^2 K l^2

We can make a regular magic hourglass using the same squares,
but with M and N different from -E and K and both positive.

The following
assumes f is larger than d. Since j^2 is positive and is the smallest
entry, M and N must both be positive.

d^2 j^2 g^2

M h^2
N

i^2 f^2 l^2

Some 6-square configurations have many ways of rearranging
squares to get different values for the other 3 entries.

But 7-square configurations
are more limited.

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