THE FOUR COLOR MAP PROBLEM

Introduction
This game is based on a simple idea: draw a map or any picture as complicated as you wish and color each region using the fewest possible number of colors, the only requirement being that regions sharing a common border must receive different colors.

It took over a hundred years for mathematicians to prove that four colors were sufficient, no matter how complicated the map. This was verified or proved, as we say in mathematics, by K. Appel and W. Haken in 1976 making substantial use of the computer to classify thousands of configurations. An interesting account of their story is available in the popular science magazine "Scientific American", October 1977.



Software
Here is how to download the software, together with some technical information.




How to play
Ten pages of six maps each are provided to color, and are presented in increasing levels of difficulty. We believe however, that a truer feeling for the problem can be obtained only by drawing the maps themselves, testing ideas, and several drawing tools are provided for that purpose.

After each region is colored, the computer will verify that neighboring regions received different colors. This might take a few seconds depending on the complexity of the map and a shaded banner at the top of the screen will blink with the message "checking your map". A display warning will appear if two neighboring regions have received the same color. When the map is completed, the computer will count the number of colors used and display one of a variety of messages evaluating the results.

The Commands
INFO: A quick explanation of the game and other commands.
DRAW: The mode "NEW" will clear the drawing board to draw a new map. Drawing tools will appear to help you draw a map. These include free drawing, straight lines, triangles, rectangles and circles.
The mode "EDIT" will let you add drawing to your map, but only on a white background to avoid creating neighboring regions of the same color.
PAINT: In the mode "COLORS", you have six colors available to color your map; they are selected by clicking the can of your choice.
The mode "WHITE" lets you erase the colors on your map for editing or recoloring.
UNDO: You can remove the last drawing performed, or the last paint while coloring.
MAPS: A set of six sample maps are available for each of ten pages, presented in increasing levels of difficulty.
SAVE: One map, completed or in progress, can be saved for each sample map provided. Use the keyboard to type a title.
QUIT: Quit the game to return to the main menu.


THE GAMES

COLORFUL MATHEMATICS

BACKGROUND

IS THIS REALLY MATHEMATICS?

TEACHER'S CORNER