错标水果袋
Mislabeled Bags
题目详情
有三个水果袋：一袋全是苹果、一袋全是橙子、一袋是苹果橙子混合。
每个袋子上分别贴了“Apples / Oranges / Mixed”的标签，但三个标签全都贴错。
你可以从任意袋子取出水果若干次来判断。
问：最少需要取出几次水果，才能确定每袋真实内容并纠正全部标签？
There are three bags of fruit. One has only apples, one has only oranges, and one has a mix of apples and oranges. Each bag is labeled (Apples, Oranges, or Mixed), but all labels are incorrect. You can pick any fruit from any bag (any number) to figure out which is which. What is the smallest number of fruits you need to draw to correctly relabel all bags?
解析
只需要取 1 次。
从标着“Mixed”的袋子取出 1 个水果。由于标签一定错，该袋不可能是混合袋，只可能是“全苹果”或“全橙”。
取出的水果是什么，就确定该袋是什么；剩下两袋也可根据“标签全错”逐一推出。
Original Explanation
Just draw 1 fruit from the bag labeled “Mixed.” Since its label is wrong, that bag must contain either only apples or only oranges. The single fruit you draw tells you which (apple or orange). Then, by logic of incorrect labels, you deduce the contents of the other two bags.