Traffic Jam Activity

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Teacher Lesson Plan

Here's the problem, which is also sometimes called Traffic Jam:

There are seven stepping stones and six people. On the three lefthand stones, facing the center, stand three of the people. The other three people stand on the three righthand stones, also facing the center. The center stone is not occupied.

Everyone must move so that the people originally standing on the righthand stepping stones are on the lefthand stones, and those originally standing on the lefthand stepping stones are on the righthand stones, with the center stone again unoccupied.

1. After each move, each person must be standing on a stepping stone.
2. If you start on the left, you may only move to the right. If you start on the right, you may only move to the left.
3. You may "jump" another person if there is an empty stone on the other side. You may not "jump" more than one person.
4. Only one person can move at a time.

You have tried this activity using two manipulatives (your bodies and the small plastic people). Now try it using the computer. Go to:

Be sure to manipulate the various options that Mike Morton has made available, including:

1. background color
2. foreground color
3. level of difficulty
4. show history and redraw history

Look for a pattern. What do you see? Are there any rules to completing this activity sucessfully? What are they?

1. What if there are only 2 people and 3 spaces?
   How many moves does it take for the two people to exchange positions?
2. What if there are 4 people and 5 spaces?
   How many moves does it take for 4 people to exchange positions?
3. What about 6?
4. What about 8?
5. What about 10?
   .....
   
6. Can you find a pattern for any number of people?