Activity of the Month
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Each month the Math Forum sponsors a student activity that can be done locally and shared globally. There are:
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 PlayPlayers 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 constraints:
1 2 3 -> <- 4 5 6
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 one person) into the space.
Object of the game:
To move from a configuration that starts out as
1 2 3 4 5 6to:
4 5 6 1 2 3
in the most economical way you can find, using the minimum possible number of moves.
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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