据鸽子洞原理，有2个数字必然相同。
By the pigeonhole principle, two of the Numbers must be the same.
另外一种版本的鸽子洞原理迟早也能碰到。
There is another version of the pigeonhole principle that comes in handy.
由鸽子洞原理，至少有2只有相同的颜色。
By the pigeonhole principle, at least two must be of the same color.
鸽子洞原理（更为广义）
令人惊奇的是，这同样是鸽子洞原理的运用！
换句话说，存在超过一个鸽子对应于一个鸽子洞的一个值。
In other words, there has to be some value of more than one pigeons per pigeonhole.
重新设想将鸽子装入鸽子洞，再设想一下平均值。
Consider again the problem of stuffing pigeons into pigeonholes and consider the average.
现在我们对鸽子洞原理有了较好的理解，现在来是怎么运用的。
Now that we have a good grasp on the pigeonhole principle, let's see how it can be used.
现在我们对鸽子洞原理有了较好的理解，现在来是怎么运用的。
Now that we have a good grasp on the pigeonhole principle, let's see how it can be used. Here are 16 of my favorite applications, categorized by difficultly.
上面的“鸽子洞”储物格可以直接放在桌子表面，也可以挂在墙上。
The pigeon-hole unit is available as an option and can be placed directly on the surface of the desk or wall mounted as shown.
根据鸽子洞原理，其中的2只火鸡体重最接近于精确到百万分之一磅的数值。
By the pigeonhole principle, two of those turkeys must have the same weight to the nearest millionth.
让人感觉不可思议的是，结果都产生于对将鸽子塞入鸽子洞现象的基本理解。
Amazingly, all the results come out of a basic insight from stuffing pigeons into pigeonholes.
根据鸽子洞原理，这个点要么至少与其它三个点相连，要么至少没有与其它三个点相连。
By the pigeonhole principle, the point is either connected to at least three other points or not connected to at least three other points.
鸽子洞原理是分析数学组合的有力工具。但是其概念简单，可以通过以下具体的问题加以阐述。
The pigeonhole principle is a powerful tool used in combinatorial math. But the idea is simple and can be explained by the following peculiar problem.
立面抽象的设计回应了展馆内部的鸽子洞书架和展柜的图案，以及五个展览体块的图案。
The abstract design of the facade is echoed in the pattern of pigeon-hole shelving and cabinetry inside the galleries, as well as five exhibition boxes.
回答是肯定的，但存在一个定式，即无论鸽子是怎样装入的，必然有一个鸽子洞要装入2个以上的鸽子。
The answer is yes, but there is one catch.The catch is that no matter how the pigeons are placed, one of the pigeonholes must contain more than one pigeon.
鸽子洞原理认为，如果有超过n只鸽子要放入n个鸽子洞中，有一些鸽子洞就要装进2个以上的鸽子。
The pigeonhole principle states that if more than n pigeons are placed into n pigeonholes, some pigeonhole must contain more than one pigeon.
现在我们对鸽子洞原理有了较好的理解，现在来是怎么运用的。以难易程度分类，我喜欢的有16种。
Now that we have a good grasp on the pigeonhole principle, let"s see how it can be used. Here are 16 of my favorite applications, categorized by difficultly".
假如27个单词能以26个不同的英文字母中的一个开头（类同于将27个”鸽子“”放入26个鸽子洞中），根据鸽子洞原理，必有2个单词以同一字母为首。
There are 27 words or “pigeons” that can start with one of the 26 different English letters or “pigeonholes. ” By the pigeonhole principle, two of the words must start with the same letter.
假如27个单词能以26个不同的英文字母中的一个开头（类同于将27个”鸽子“”放入26个鸽子洞中），根据鸽子洞原理，必有2个单词以同一字母为首。
There are 27 words or "pigeons" that can start with one of the 26 different English letters or "pigeonholes. " By the pigeonhole principle, two of the words must start with the same letter.
圆屋顶上有个洞，洞里有只鸽子。
圆屋顶上有个洞，洞里有只鸽子。
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