Here's the problem:
There are seven stepping stones and six people. On the three left-hand stones, facing the
center, stand three of the people. The other three people stand on the three right-hand
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 right-hand
stepping stones are on the left-hand stones, and those originally standing on the
left-hand stepping stones are on the right-hand stones, with the center stone again
unoccupied. Can you find the least number of moves?
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.
Try it!:
___________ ___________ ___________ ___________ ___________ ___________ ___________
Explore possible solutions and determine the least number of moves required to solve the
problem. Use members of the group and play the traffic jam and then use the two-colored
discs to explore. What is the least number of moves for 6 people?
Dr. Cyndi Osterhus
costerhus@carolina.rr.com
704-239-7647
Traffic Jam Game - Java applet : http://mathforum.org/alejandre/java/jam/Jam.html
Be sure to manipulate the various options that Mike Morton has made available,
including: color, level of difficulty and show history and redraw history
Look for a pattern. What do you see? Are there any rules to completing this activity
successfully? 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?
5. What about 6? 8? 10?
6. Can you find a pattern for any number of people?
Number of People
Least number of Moves
Dr. Cyndi Osterhus
costerhus@carolina.rr.com
704-239-7647
There's another version of Traffic Jam at the Math Forum if you want more fun:
http://mathforum.org/workshops/sum96/traffic.jam.html.
Handout retrieved from http://mathforum.org/alejandre/frisbie/jam.handout.html, June 9, 2009
Slight modifications made to the activity retrieved from
http://mathforum.org/alejandre/frisbie/student.jam.html, June 9,2009.
Dr. Cyndi Osterhus
costerhus@carolina.rr.com
704-239-7647