**NYC Hardest Logical Deduction Puzzle - 21 January**

You are hanging around in NYC when a person approaches you.

"Leaving the bald people aside, I can bet a hundred bucks that there are two people living in NYC who have same number of hairs on their heads," he says to you.

You say that you will take the bet. After talking to the man for a couple of minutes, you realize that you have lost the bet.

What did the person say to you that proved his statement ?

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Typical example of the very powerful and very useful in Mathematics: "Principle of the Pigeonhole" (or Pigeonhole principle ,or "Schubfachprinzip" the original term used by the great mathematician Dirichlet).

ReplyDeleteIf n+1 pigeons have to be placed in n pigeonholes, then at least one hole has 2 pigeons. Or even simpler stated: If you have 3 children ,at least 2 are boys (or girls) :-)

Hair case: Since the maximum number of discrete hairs a person can have is about 300.000 , but let's assume even 500.000 ,that means that not only 2 ,but at least 20 (assuming NYC has a population of let's say 10 millions) New Yorkers have exactly the same number of hairs... :-)

And there is no need at all to "leave the bald people aside ". No influence on the problem whatsoever. 0 is a totally normal number of hairs ,and does not affect the validity of the deduction.

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