Procedure: A group of people stand in a circle. They are numbered in a clockwise direction beginning at number 1 through to the last person (e.g., through to number 20 if there were 20 people). Person 1 starts with the tennis ball and taps person 2 on the shoulder. Person 2 must sit down. The tennis ball is passed onto the next standing person (person 3 in this case). This person touches the shoulder of the next standing person with the tennis ball. Each person tapped on the shoulder must sit down, and the tennis ball is passed onto the next person standing. After the tennis ball has been passed around the circle once, it continues to go around the circle until there is only one person standing.

Problem:

1. Start with 6 people in the group. Do the above procedure. Which person is the last one standing? How many times did that person hold the tennis ball?
2. Repeat the procedure this time starting with 13 people in the group. Which person is the last one standing? How many times did that person hold the tennis ball?
3. Imagine the circle begins with 37 people and the procedure is done. You wonder who will be the last one standing. Which of the following people do you know for sure cannot be the last one standing? Explain how you know this.

   Person #:   A. 1    B. 37    C. 11    D. 18    E. 19

4. If the procedure begins with 73 people in the circle, how many times do you think the last person standing will hold the tennis ball? Explain your answer.
5. If the procedure begins with 73 people in the circle, predict the number of the last one standing. Explain how you made your prediction.

Materials: people, tennis balls, pencil, paper, calculator

Extra Questions: You can try this procedure beginning with any number of people. Who is the last one standing if you begin with 1500 people in the circle? How many times will that person hold the tennis ball during the procedure?

Do you know what a binary search is? If not, see if you can find out. Describe how the tennis ball procedure is similar to a binary search. Describe how it is different.

Patterns, critical and creative thinking, communication

  Activity Type:

Group      Individual 

  Assessment:

Scale:    Levels 1-5   
Self     Peer     Teacher 
Include in your portfolio?
Yes     No     Optional 
Toward Your Marks?
Yes     No     Optional 

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