The pigeonhole principle (more generalized)
鸽子洞原理（更为广义）
Amazingly, this is also about the pigeonhole principle!
令人惊奇的是，这同样是鸽子洞原理的运用！
By the pigeonhole principle, two of the Numbers must be the same.
据鸽子洞原理，有2个数字必然相同。
The pigeonhole principle is a important principle in combinatorics.
鸽巢原理是组合学中一个非常重要的原理。
By the pigeonhole principle, at least two must be of the same color.
由鸽子洞原理，至少有2只有相同的颜色。
There is another version of the pigeonhole principle that comes in handy.
另外一种版本的鸽子洞原理迟早也能碰到。
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。
By the pigeonhole principle, two of those turkeys must have the same weight to the nearest millionth.
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。
Using essentially the same argument, we can prove the following more general statement of the pigeonhole principle.
用实质上相同的论证，我们可以证明下面关于鸽巢原理更一般的结论。
By the pigeonhole principle, the point is either connected to at least three other points or not connected to at least three other points.
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。
The pigeonhole principle states that if more than n pigeons are placed into n pigeonholes, some pigeonhole 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。
You can say that the proof USES nothing beyond elementary matrix theory, repeated use of the triangle inequality, and the pigeonhole principle.
你可以简要地说其实证明就是初等矩阵理论，三角不等式和鸽笼原理的运用。
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.
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。
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.
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".
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。
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.
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。
应用推荐