SOLUTION: Discrete Math: 1. Among the residents of New York City (population 7,000,000), must there be at least two people with the same number of hairs on their heads, why or why not? As

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: Discrete Math: 1. Among the residents of New York City (population 7,000,000), must there be at least two people with the same number of hairs on their heads, why or why not? As      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 434207: Discrete Math:
1. Among the residents of New York City (population 7,000,000), must there be at least two people with the same number of hairs on their heads, why or why not? Assume the average head contains 300,000 hairs.
2. Show that in a group of 85 people at least 4 must have the same last initial.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We can assume that everyone must have between 0 and, say, 999,999 hairs. With an arbitrarily large population, there must be at least two people with the same number due to the Pigeonhole principle.

There are 26 letters for the last initial. If there are at least 79 people (3*26 + 1), then by the Pigeonhole principle, there must exist four people with the same last initial.