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Minimum number of coins on a chesstable

Source: Moldova IMO-BMO TST 2003, day 2, problem 4

August 16, 2008

Problem Statement

On the fields of a chesstable of dimensions n×n n\times n, where n≥4 n\geq 4 is a natural number, are being put coins. We shall consider a diagonal of table each diagonal formed by at least 2 2 fields. What is the minimum number of coins put on the table, s.t. on each column, row and diagonal there is at least one coin? Explain your answer.
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