送交者: 红琴 于 July 28, 2009 10:50:14:
回答: 【其它】lala请帮个忙！是一个概率的问题。 由 老六 于 July 26, 2009 21:48:00:
对不起大家，因为我的中文没有好到能解释这个问题，所以我不得不用英文来解释。
This problem is an example of a statement in mathematics called the Pigeonhole Principle. This principle states that if there are 2 natural numbers n and m where n>m, and n items are placed into m pigeonholes, then at least one pigeonhole will have more than one object. In order to understand it, let's start with a few basic examples.
The most basic example is that if there are a family of 3 people, at least 2 of them must have the same gender.
If there are 4 people and 3 rooms, and the people are arbitrarily selected to each room, what is the maximum amount of people that are sure to be in one room?
Obviously this answer is 2, because you can seat 1 person per room, and have one person left over, and he/she must be placed into one of the rooms for a total of 2 people.
Why can't it be 3 or 4? The chances of 3-4 people sitting in one room is NOT GUARANTEED. It is possible that there can only be [2,1,1] people sitting in the rooms.
If you have 5 balls of either yellow or red color, what is the maximum amount of balls of the same color you are sure to have?
You may be thinking 1 or 2, but if you are, then you're not thinking about the other color. If you have 1 yellow ball, then you have 4 red balls, so the answer is 4, right? Well, it is possible you have 2 red balls, and so you'll have 3 yellow balls, which is even less than 4.
The answer is 3.
Knowing these concepts, you can figure out the maximum number of items that you are sure to find by simple division. n/m, and add 1 unit if there is a remainder. So from the previous examples, 4/3 = 1 R1, or 1+1=2. 5/2 = 2 R1, or 2+1=3. (doesn't matter if there is more than one in the remainder, you only add 1)
So in this problem, you know there 4 rooms, so the maximum you are sure to have in each room is 100/4 = 25. And out of these 25 people they are either blond or red, so 25/2 = 12 R1, so 12+1=13.
13 people. <(^.^<)