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MathNet 2010 — Part 01 Question 133

Math Olympiad Vault · MathNet 2010 — Part 01

Question 133

Given a $3n \times 3n$ table with one of two signs "+" or "-" in any of its cells. Per move one can replace the signs in all cells of some row (or of some column) by the opposite signs. At the beginning there is exactly one minus in the table (all other signs are pluses). After some moves the table with exactly 36 minuses is obtained.
Find all possible values of $n$.