September "Bravos" to Steve Weimar, Sarah Seastone, and Sum96 for the suggestions and examples, and Mike Morton for the nifty Applet.

## Traffic Jam## Activity of the Month## September 1996 |

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Each month the Math Forum sponsors a student activity that can be done locally and shared globally. There are:

- discussion suggestions for the teacher or student activity leaders,
- examples of approaches to the activity,
- ways to share what you do and learn,
- and here's a link to a Java Applet that simulates this puzzle.

Traffic Jam is a game for any number of people, but it's probably best begun with an even number and 1, 2, or 3 on each side.

## How to Play

Players divide into two groups and line up facing each other with one open slot in the middle:The two groups exchange places, observing the following ## 1 2 3 -> <- 4 5 6

constraints:

- If the slot immediately in front of or behind you is empty, you may step into it. There is always only one slot empty.

- If there's a space on the other side of a person next to you, you may step around that person (but only around
oneperson) into the space.

## Object of the game:

To move from a configuration that starts out as

## 1 2 3 4 5 6

to:## 4 5 6 1 2 3

in the most economical way you can find, using the minimum possible number of moves.

## Discussion suggestions:

- What's the minimum number of moves necessary for two people on a side? for three people on a side?
- How is this minimum number of moves related to the number of people on a side?
- What formula can account for the minimum number of moves for any number of people on a side?
- Is there a pattern in the different kinds of moves people make - for instance when they move directly into an empty slot and when they move around another player?
- Do you find a pattern related to the number of people on a side?
- Is there a simple set of directions a group can follow to accomplish the task in the minimum number of moves?

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