1. Consider a game with two players in which the rst player starts with the number 1. The second player must say 2; 3 or 4. Then it is player 1's turn, who must increase the previous stated number by 1; 2 or 3. In the next turn; player 2 must follow the same rule, i.e. increase the previous stated number by 1, 2 or 3. Players are not allowed to state numbers greater than 21. and the person who is forced to say "21" loses the game. 1.1. Is there any last but one move that guarantees the victory to a player? Explain. 1.2. Using your answer from the previous question and backward induction, find out a winning strategy in this game. 1.3. Is the winning strategy available to all players? Explain. 2. In the game Countdown, we start with just one large pile of 100 stones. At hisfher turn, a player can only remove up to 1D stones at a time. Can you figure out the winning strategy for Countdown, when the winner is the player who makes the last move, so there are no stones left after that move? If you start with 10!] stones, does the rst or the second player have a winning strategy