You can attract it without lifting the pen. However then i tried to attract two houses side-to-side :

Then i realized you cannot actually execute it there is no lifting the pen. Ns tried any type of ways i could. You finish up all the time with one heat missing.

That"s why i was wonder whether over there existed a proof that ns cannot actually execute it.

You are watching: Draw a house without lifting pencil

I heard that we need to count the total number of lines and also the number of intersections and also that this number tells us something but I am not certain at all.

I to be a an initial year cg-tower.coms college student so i haven"t learned graph theory yet !

Thanks !

This sounds prefer a good excuse to research (just a little) graph concept to me! inspect out the conclusions that Euler in this well known problem. It need to tell you every you need to understand (and more). In particular, the second figure has actually $4$ nodes of odd degree (that is, an odd number of segments having actually that typical endpoint)--the external bottom corners and also the 2 nodes where the "houses" meet--so it cannot be traced there is no lifting the pen or retracing at the very least one segment that the path.

Take a peak with 3 edges. Assume you carry out NOT begin there. Then there is a first time you will certainly reach this vertex, through among the possible paths resulting in it. It i will not ~ be the end of her drawing because two various other paths are not however traversed. Thus, you will leave this vertex, with a second adjacent path. As a result, once you traverse the third path some time, girlfriend won’t have the ability to leave this vertex since no untraveled courses will it is in available. In various other words, your drawing will have actually to end here.

**So, we confirmed that if friend don’t start at a crest (with odd number of edges), friend will have actually to end there.**

This is likewise true around vertices with 5 edges. Thus, if any type of graph has an ext than two vertices v odd degrees, you won"t have the ability to draw it.

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