Path to the Stars

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
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Is it possible to draw a 5-pointed star without taking your pencil off the paper?

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Path to the Stars


Is it possible to draw a $6$-pointed star in the same way without taking your pen off? Remember that you shouldn't join points that are right next to each other and you can't go over the same line twice. Your lines must run straight from one point of the star to another.

Have a go:

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Path to the Stars


What about $7$-pointed and $8$-pointed stars?

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Path to the Stars


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Path to the Stars


Do you think you'll be able to draw a $9$-pointed star without taking your pencil off? Why?