MathDB

For a given integer

n \ge 4

we examine whether there exists a table with three rows and

n

columns which can be filled by the numbers

1, 2,...,, 3n

such that

\bullet

each row totals to the same sum

z

and

\bullet

each column totals to the same sum

s

. Prove: (a) If

n

is even, such a table does not exist. (b) If

n = 5

, such a table does exist.
(Gerhard J. Woeginger)

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