Poster Solution  

The 3 drawing in one go challenge 

The first two pictures can be drawn in one go, the last one cannot. For the first picture, one must start drawing in the bottom left or bottom right corner. For the second picture one can start anywhere!

Here is why:

When drawing the figure and moving into the corner, one must be able to move out of that corner again, otherwise one is stuck. So, there must be an even number of lines ending in a corner. The only exception is the starting corner and the ending corner.

So: if a figure has at most two corners, in which an odd number of lines ends, then it can be drawn in one go. If it has more than two such corners, then it cannot be drawn in one go. Here is the count for all corners in all three pictures:

As we can see: the first picture has exactly two corners in which an odd number of lines ends. The second picture has no such corners, and the third picture has four such corners. That explains why only the first two can be drawn in one go.