2010年Puzzleup数学竞赛−第05题: Nine Balls

castelu

Nine Balls

    You have nine balls, three of which are slightly heavier, and three ofwhich are slightly lighter than the normal three. All three balls ineach group have the same weight. All nine balls are identicalotherwise. Your mission is to determine the group of every ball using apair of scales.

    How many weighings are needed in order to ensure the accomplishment of your mission?

Notes:
1. The difference of weight between the heavy and normal balls is notnecessarily equal to the difference of weight between the light andnormal balls.
2. The scales show only which side is heavier; it does not show the difference of weight.

zyzme

                                  9个小球
你有9个小球，平分为三组A，B，C，其中，A组比C组略重，B组比C组略轻。

每组的3个小球重量相等。除此之外，这9个小球完全相同。

你的任务是用一副天平确定出每个小球所在的组。

为了保证完成任务，你至少需要称量多少次？

注释：
1.较重的小球和正常小球在重量上的差别不必与较轻的小球和正常小球在重量上的差别相等。
2.这个天平只能显示哪一侧更重，不能显示重多少。