# 1, 2, 3, 4, 5, 6, 7, 8, 9

Discrete Mathematics Level pending

Victor's mathematics teacher gave him a $$3 \times 3$$ grid filled with the numbers $$1, 2, 3, 4, 5, 6, 7, 8$$ and $$9$$ in an unspecified order, with each number appearing only once.

Given any row

$\begin{array}{ | l | c | r | } \hline a & b & c \\ \hline \end{array}$

or column

$\begin{array}{ | l | c | r | } \hline d \\ \hline e \\ \hline f \\ \hline \end{array}$

in the grid, Victor is allowed to perform the following operations:

Row:

• $$a+k$$, $$b-k$$, $$c-k$$

• $$a-k$$, $$b-k$$, $$c+k$$

Column:

• $$d+k$$, $$e-k$$, $$f-k$$

• $$d-k$$, $$e-k$$, $$f+k$$

with $$k$$ being a non-negative real number and that the numbers in the grid must always be greater than $$0$$.

Given that it is possible to perform row and/or column operations such that all the numbers in the grid are equal to a positive real number $$N$$, find the maximum value that $$N$$ can take.

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