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MathNet 2006 — Part 03 Question 70

Math Olympiad Vault · MathNet 2006 — Part 03

Question 70

162 pluses and 144 minuses are placed in a $30 \times 30$ table in such a way that each row and each column contains at most 17 signs. (No cell contains more than one sign.) For every plus we count the number of minuses in its row and for every minus we count the number of pluses in its column. Find the maximum of the sum of these numbers.