Pat has a number of counters to place into the cells of a 3 3 grid like the one shown. She may place any number of counters in each cell or leave some of the cells empty. She then finds the number of counters in each row and each column. Pat is trying to place counters in such a way that these six totals are all different. What is the smallest total number of counters that Pat can use?
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Junior Mathematical Olympiad 2011 (2011)
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