83 people are in a class, each holding a coin in one hand. 25 have one in their right hand and 58 have one in their left hand, but you don't know which is which.
Your task is to split the people into two groups such that the same number in each group has a coin in their right hand, and you can do this in two steps:
Separate the people into two groups with n people in the smaller group.
Tell m people, including however many you like in either or both groups, to switch the coin to the opposite hand.
Q: What is n+m?