Traffic Jam Activity

## Student Page

Teacher Lesson Plan || Suzanne's Mathematics Lessons

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.
The challenge: exchanging places
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.
The rules:
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:

(Use the file traffic.mws to experiment with this)

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?

2. How many moves does it take for the two people to exchange positions?
3. What if there are 4 people and 5 spaces?

4. How many moves does it take for 4 people to exchange positions?