Indirect Proof Warm-Up Activity

Good introductory activity before beginning Indirect Proofs.

Warming-Up for Indirect Proofs (adaptation of an activity seen at a conference many years ago) Materials:  3 colored index cards (2 cards of the same color                         and one card of a different color).  For this                         write-up, we have 2 red cards and one blue.                     scotch tape  Directions: Show the three colored cards to the class.  Ask for two volunteers to come forward to participate in an experiment.

• Instruct the class that they must remain silent during the experiment.
• Ask the two volunteers to face the class while you tape a card to each student's back.  Do not let the student volunteers see which colored card you are taping to them.  Tape the two red cards of the same color to the two volunteers and hide the other blue card.
• Each volunteer may look at the card taped to the other volunteer, but may not speak of (or indicate in any manner) the color. 
• Ask the volunteers to tell you when they think they know what color card is taped to their back.  They must support their answer with a method of reasoning (not simply a guess).
• Wait for the volunteers to ponder their situation.
• If the volunteers cannot arrive at a means of determining the color of their individual cards, ask if someone from the audience can determine a method of reasoning.

The reasoning is indirect.
1.  You are more likely to have a red card.
2.  Assume the opposite.  Assume you have the one blue card.
3.  If you have the one blue card, the other volunteer, upon seeing your blue card, would immediately
     know that he/she had a red card.
4.  Since the other volunteer is not responding immediately, you do not have the blue card.
5.  You have a red card.