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Minimum sum if lower bound for crosses is given

Source: Bundeswettbewerb Mathematik 1972, round 1, problem 1

May 1, 2007

Problem Statement

There's a real number written on every field of a n×nn \times n chess board. The sum of all numbers of a "cross" (union of a line and a column) is ≥a\geq a. What's the smallest possible sum of all numbers on the board¿
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