### Brain Teasers

# Line Drawings

We all know and love those drawing puzzles in which you have to draw a symbol without retracing or lifting your pencil. The quickest way to check if a symbol can be drawn with such restrictions is to count the vertices in which an odd number of line segments meet.

If there are more than three vertices in which this occurs, the symbol cannot be drawn.

Can a symbol have only one vertex in which this occurs?

If there are more than three vertices in which this occurs, the symbol cannot be drawn.

Can a symbol have only one vertex in which this occurs?

### Hint

Odds and ends### Answer

It cannot.There must be an even amount of vertices in which this occurs, as these signify the ends of a line segment. It cannot have only one, as a line segment with one ending does not exist.

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## Comments

What????

I made this and I can't understand it.

Ha ha! Well that's honest!

I said, "Yes." I drew an equilateral triangle, starting at the top, drew the sides, came back to my staring point, and then drew a median dropping to the base opposite. The median bisected the original triangle, creating two interior triangles and their additional two-line vertices. So I've drawn a bisected triangle keeping my pencil on the paper. The median line has at one end a vertex with three line segments, an odd number, and the only such vertex. At the other end the median line segment joins a straight line. There are two vertices there, the corners of the two interior triangles, but I can't see calling the straight line a vertex of three line segments.

I'm not a math person, and I figure there must be something about the terms used that I don't understand. Can someone help me here?

I'm not a math person, and I figure there must be something about the terms used that I don't understand. Can someone help me here?

Theriddler,

An odd vertex is present at the intersection of the median and the base. It creates three angles.

An odd vertex is present at the intersection of the median and the base. It creates three angles.

The original puzzle is mis-stated. It should read "If there are more than two of these...", otherwise it even breaks the rule in the answer.

As you probably know, I posted no less than FIVE logic teasers. You should totally check them out.

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