Extreme Puzzle Fun

[nick_t]

Try to solve this puzzle:

So the rules are:

- you have to draw a single line
- if a line (on the diagram) connects two points, you must cross it! There are 16 of these
- you cannot cross the lines conencting two points more than once
- you can cross your own line as many times as you want

 

[Dan]

It's basically a version of the bridges of Venice (or maybe it's some other city) problem.

I don't think it's solvable beause you have 3 enclosed areas with an odd number of enterance/exit points. That means that you can't go through all of the connecting lines that enclose that area without either starting inside it or ending inside it. Since there is only 1 endpoint and 1 start point, it can't be done.

 

[nick_t]

It's basically a version of the bridges of Venice (or maybe it's some other city) problem.

I don't think it's solvable beause you have 3 enclosed areas with an odd number of enterance/exit points. That means that you can't go through all of the connecting lines that enclose that area without either starting inside it or ending inside it. Since there is only 1 endpoint and 1 start point, it can't be done.

I concur with you wholeheartedly. However, I am still waiting to be amazed by some "abstract" solution since I've heard there is a possible solution to this crux.

 

[Dan]

Here, I annotated the diagram to explain.. sort of. I just drew cirlcles to point out where all of the points are, and hatches to show where you have to cross each line segment. When you add up the numbers on each of the enclosed spaces, you see that three of them have odd numbers. 4 actually if you count the outer boundary