2010年Puzzleup数学竞赛−第13题: Colored Balls

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Colored Balls

    You have 111 balls of five different colors. There is at least one ballof each color. You are placing these balls randomly into 11 boxes, onthe condition that each box contains at least one ball. You can deducethat in any such placement and any such distribution of colors amongthe 111 balls, at least one of the boxes must contain at least X ballsof the same color.

    What is the maximum possible value for X?