write down the names of the 800,000 people.
Construct 200,000 boxes.
For each person, put the name in the box that corresponds to his hair count.
Even if the 1st 200,000 names have unique hair counts, then the 200,001st name will have to go into a box that is no longer empty.
Similarly, there must be at least 4 people with the same hair count, since the names might be evenly distributed among the 200,000 boxes. Any other non-uniform distribution would ensure that there were more than 4 people with the same count.
In the 17th century, there were more than 800,000 inhabitants of Paris. At the time, it was believed that no one had more than 200,000 hairs on their head. Assuming these numbers are correct and that everyone has at least 1 hair on their head, show that there had to be two Parisians with the same number of hairs on their heads. Can you find a better number than two?
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