![If you have 11 pigeons flying into 10 pigeon-holes, then what can you say about the resulting arrangement of pigeons? Well you can be sure that there will be at least one pigeon-hole with more than one pigeon in it. It’s impossible for all pigeon-holes to end up with less than 2 pigeons in them. This principle in mathematics is called the pigeon-hole principle, and is a really useful tool for proving things. For example, there are two non-bald people in London with exactly the same number of hairs. There are more people (pigeons) than there are possible numbers of hairs (pigeon holes). [more] [code]](http://24.media.tumblr.com/tumblr_lmdl1qH1Kw1qfg7o3o1_400.gif)
If you have 11 pigeons flying into 10 pigeon-holes, then what can you say about the resulting arrangement of pigeons? Well you can be sure that there will be at least one pigeon-hole with more than one pigeon in it. It’s impossible for all pigeon-holes to end up with less than 2 pigeons in them. This principle in mathematics is called the pigeon-hole principle, and is a really useful tool for proving things. For example, there are two non-bald people in London with exactly the same number of hairs. There are more people (pigeons) than there are possible numbers of hairs (pigeon holes). [more] [code]
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^_^ my favorite way of stating this principle is this way: imagine you have 11 holes, and 10 pigeons. Then you know that...
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I SO remember my CMSC56/57 right now. Discrete Math
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you’re not following Matthen… why?...Wikipedia for math and science.
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