You play a game similar to one we discussed during the lecture.Two players are taking stones from a heap in turn. Each player can take $1$ to $2$ stones at a time. However, this time the player who takes the last stone loses. Both players play with an optimal strategy, so that a player always wins whenever it's possible.Formulate a theorem that will predict a winner based on a number of stones N in the heap. Now prove your theorem using math induction. How many base cases do you need? Don't forget to prove them before you take the inductive