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A triangle is divided into nine smaller triangles, where counters with the number zero are placed at each of the ten vertices. A movement consists of choosing one of the nine triangles and applying the same operation to the three counters of that triangle: adding a unit or subtracting a unit. The figure illustrates a possible movement. We shall call the integer number n dominant if it is possible, after a few moves, to obtain a configuration in which the counter numbers are all consecutive and the largest of these numbers is

n

. Determine all dominant numbers. https://cdn.artofproblemsolving.com/attachments/7/3/731160e6e9a2b3292a31c4555d4adbc7028596.png

6

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