Numbers Game

               During one of my torus to Canada, I come across a very interesting game partivipated by two players.

              A group of match sticks is placed on the table and then it is reduced in turn by each player by removing from the group at least 1 but not more than 4 match sticks.

             The player who takes the last match stick is the winner.

              If there is a group of 17 match sticks on the table how would you make your first move, if it was your turn and how would you continue to play to win?

Answer :     The person who moves when there are 5 matchsticks will lose the game, become if you remove one match stick the other person will take the remaining 4, And if that person takes two then you will take remaining 3, so on and so forth . Therefore, the person who moves when there are 10 or 15 matchsticks will lose.

                  The only correct way to make the first move is to take away 2 matchsticks and reduce the pile to 15, then no matter what your opponent does on his move, you reduce the pile to 10, then to 5 and lastly you take the remaining matchsticks.