# Nine Dots

### From Mycoted

Imagine the pattern of dots below drawn on a sheet of paper.

Your task is to join all nine dots using only four (or less) straight lines, without lifting your pencil from the paper and without retracing the lines.

The standard Answer | |
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Many people who try to solve this problem start with the assumption that the lines must be inside the square formed by the dots. But this was never stated in the original problem! | |

There is always more than one right answer to many problems. Here are some other ways you could have solved the Join the Dots problem:

Another Answer | |
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If we had a thick pencil, we could join the dots with just three lines. | |

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Why stop at three lines? Why not take a very thick pencil and do the job with just one line??? | |

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Even with a thinner pencil, we could still make do with three lines by folding the paper so that the dots were closer to each other. | |

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If we laid the paper on the ground, we could draw one very long line which encircles the Earth three times, joining one row of dots each time | |

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And if that sounds a bit far-fetched, we could do the same thing by rolling the paper into a cylinder. | |

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Yet another solution is to fold the paper in three, so the rows of dots all line up, and fold it again and poke the pencil through! | |

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In mathematical terms, parallel lines are sometimes considered to "join" at infinity, so here's a solution that uses just three lines! | |

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Of course, we could question the assumption that we have to follow the rules! This solution uses five lines ;) | |

Another Answer... | |
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There are at least another 5 solutions I have come across - can you think of others. | |