Multilingual Hedge Fund - Combinatorics Puzzle
Source: Quantnet Forums
Problem:A hedge fund has 70 employees. For any two employees X and Y there is a language that X speaks but Y does not, and there is a language that Y speaks but X does not. At least how many different languages are spoken by the employees of this hedge fund?
Update: (Dec 17, 2012)
Correct answer posted by Nikhil Jain (IT BHU Alumnus 2008), Paul Wong and Tuhin (IITB 4th year student) in comments.
A very similar but more difficult problem posted a couple of years back: http://pratikpoddarcse.blogspot.in/2009/12/number-of-locks-and-keys.html