Four-Colour Darts


Four-Colour Darts is a game based upon the Four-Colour Theorem, which states that any map can be coloured using, at most, four colours. Four-Colour Darts challenges you to colour in maps that resemble dartboards using just these four colours.

Configure the dartboard by entering step sizes in the boxes at the bottom of the screen. The step sizes control the length of the segment in each ring - the smaller the step size, the greater the number of rings. Certain configurations can be selected by choosing from the drop-down list. The step sizes are in arbitrary units - the correct scaling factors will be applied automatically. The entered configuration will be simplified if it would otherwise require the drawing of extremely small arcs. Select a step size of zero to eliminate a ring entirely.

Press Restart to begin. Upon completion, the duration of the game in seconds is displayed in the centre of the board.

Select the active colour by clicking on the palette under the dartboard - the active colour is shown as a circle instead of a rectangle. Click on a segment in the dartboard to colour it. You cannot click on a segment if an adjoining segment is identically coloured. If clicking on a segment means that some other segment on the dartboard can now only possibly be coloured in one way, that segment will be filled automatically. Use grey ink to clear previously-coloured segments.

Press Complete to see the computer complete the dartboard. If you become bored waiting for the computer to generate a solution, press Restart to restart the game.

Solve looks for a solution to the dartboard defined by the current step sizes (it ignores the colourings of any game in progress) and, if successful, displays the solution in a text window. Since the solution is not displayed graphically, the entered step sizes are not amended should they imply a dartboard that cannot be drawn given a typical screen resolution.



For Programmers

Computer programmers can download the source code from here. The source code is completely free but, of course, comes with no guarantee.

Comments

Comments are very welcome and should be sent to comments@act365.com.

Acknowledgements

Thanks to Carl Ginnow for comments on problems encountered on lower-resolution displays.