Game #2

Transcript

Game #2 The Game and its Rules The Game and its Rules This is a new counting game for two players with a different target and different rules for adding numbers: The first player starts by saying a number between 1 and 10. Players take turns adding a number between 1 and 10 to the previous total. The first player to say the number 99 wins! Let’s play an example game Between your friend and you Turn 1: Player 1 (Friend) Friend says: "7" Turn 2: Player 2 (You) You add 4 and say: "11" Turn 3: Player 1 (Friend) Friend adds 10 and says: "21" Turn 4: Player 2 (You) You add 1 and say: "22" ...The game continues with you always saying the next multiple of 11... Final Turns: Player 1 (Friend) Friend is on 77 and adds 9, saying: "86" Player 2 (You) You add 2 and say: "88" Player 1 (Friend) Friend adds 10 and says: "98" Player 2 (You) You add 1 and say: "99" Player 2 wins! The Winning Strategy Just like in the game of 21, the key is to control the game by saying a sequence of "magic numbers". The Goal: To say 99. The number before 99: To guarantee you can say 99, you must say the number 88. If you say 88, your opponent can add any number from 1 to 10, which will result in a number between 89 and 98. From any of those numbers, you can add the correct amount (from 1 to 10) to reach 99. So, the first magic number before 99 is 88. The number before 88: Using the same logic, to guarantee you can say 88, you must first say 77. The next magic number is 77. The Winning Sequence The pattern here is clear: the magic numbers are all 11 apart. This is because the maximum number you can add is 10, so the key interval is 10 + 1 = 11. The winning sequence of numbers to say is: 11, 22, 33, 44, 55, 66, 77, 88, 99.