Disclaimer: Difficult Problem
Source: Amol Sahasrabudhe (Associate, Morgan Stanley) - Got his permission to put it on blog \m/ \m/
Problem: Lets consider a two player game in which a number is given. The first person gets a chance to choose a number of the form (prime-1) and subtract it from the given number. Then the second person gets a chance to do the same and so on. The person who makes the number zero wins.
So, if the chosen number is of the form (prime-1), the first person would win in the first chance. There are infinite numbers for which first person has a winning strategy. Prove that second person also has a winning strategy for infinite numbers. :)
Bonus: Given a chance to choose whether you want to be first person or second person, what would you choose?
Solution: Posted by Siddhant Agarwal (4th year, EE, IITB) in comments!