# Three Crossings Puzzle

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You are asked to maneuver the colored dots so that the board contains three line crossings.

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Contributed by: Karl Scherer (June 2015)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Introduction

Seven challenges use seven vertices, and five challenges use eight vertices.

Challenge #Lines Crossings Balls-at-rim -------------------------------------------------------- 1 7 3 7 2 7 4 6 3 7 5 4 4 7 6 3 5 7 7 6 6 7 11 4 7 7 12 5 8 8 7 6 9 8 9 5 10 8 11 4 11 8 12 3 12 8 13 6

To move a vertex (one of the seven dots), drag it and see that the connecting lines change. Here is how they change:

No matter which dot you move, the dot numbered "1" is connected to the closest dot, which is then connected to a third dot, which is the closest of those dots that are not contained in the connected chain of dots yet. Finally, the last dot remaining is connected to the first.

If you move a vertex to the rim of the board, its accompanying dot turns green.

You Check a Win

The system does not check the number of intersections of lines. There is no win message. It is easy enough to check this with your own eyes.

Controls

Click popup menu "challenge" or "" to select a task.

The next line shows the number of vertices you are given.

"line crossings" denotes the number of line crossings you have to achieve.

"dots at rim" shows how many of the dots (vertices) should be placed at the rim of the board (expert levels).

Click toggle "color" to show the dots in various colors (or just red).

Select "numbers" to see the sequential numbers of the dots.

Slider "point size" controls the size of the colored round dots.

Slider "thickness" controls the thickness of the edges connecting the dots (very useful in crowded situations, where you should keep the line thickness to a minimum).

"Solution" button: only the solution to challenge 4 is available.

## Permanent Citation

"Three Crossings Puzzle"

http://demonstrations.wolfram.com/ThreeCrossingsPuzzle/

Wolfram Demonstrations Project

Published: June 25 2015