Math 4713

Assignment 3

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

• Player 1 takes 1 chip
• Player 2 takes 2 chips
• Player 1 takes 1 chip
• Player 2 takes 2 chips
• Player 1 takes the remaining chip and wins!

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:

• At what point in the game can you tell who will win the game? Explain your reasoning.
• What strategy did you develop to help you to win the game? Explain your reasoning.
• Does the person who goes first have an advantage? Why or why not?

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:

• Comment on how you as a teacher would help children distinguish between a fair game and fair play.
• On the second page of the article, first column, third complete paragraph, the author describes three phases of development in playing this game. Reflect back over when you were playing the game. Did you go through each of these phases? Or did you go straight to the third phase? As a teacher what questions could you pose to your students to get them to move beyond the first phase?
• Both Nate and Nicholas noticed that once you leave three chips on the table you have won. Had you noticed this previously? Play the game a few more times keeping this strategy in mind. Did you improve your winning record?
• Table 1 shows the possibilities for playing the game if the first player takes 1 chip. In both cases, player 1 wins. Create a similar table for the two cases when player 1 takes 2 chips on his/her initial move.

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.