Math 4713

Assignment 3

Due Date: March 29th (for TR) and March 30th (for MW)



Take Two – Is It Fair?



Game:  Place seven chips in a row.  Two players take turns, removing one or two chips each turn.  The person to remove the last chip is the winner.


Example 1:


·        Players 1 takes 2 chips

·        Player 2 takes 1 chip

·        Player 1 takes 2 chips

·        Player 2 takes the remaining 2 chips and wins!


Example 2:



Question:  Is “Take Two” a fair game?  Does it make a difference who plays first?



To address this question, you should begin by playing the game at least 30 times with someone else.  As you play, record whether the person who went first wins or the person who went second wins.  Include this data with your project.  While playing, try to develop a strategy for winning the game.


Once you have played the game at least 30 times, answer the following:



After playing the game and answering the above questions, read the 2-page article titled, “Responses to the Take Two: Fair or Unfair? Problem” in Teaching Children Mathematics, December 1999, p. 252-53.


Answer the following:




Based on Table 1 and the table that you have created, provide a sound argument as to why this game is unfair and why the player who goes first has an advantage.