Those annoying "draw-the-sketch-without-tracing-over-the-same-line-and/or-without-lifting-your-pencil" Puzzles

This page will not explain how to solve this kind of puzzle, but instead will tell you how to spot one that is impossible to solve.

A node is either where 2 or more lines meet or cross, or where a single line ends at a point.

There are two types of nodes, even and odd. An even node has an even number of lines branching out, while an odd node has an odd number of lines branching out.

Count the number of odd nodes. If there are 2 odd nodes or NO odd nodes, then the puzzle is solvable; otherwise it is impossible.

In this drawing there are 5 nodes total, and 4 of them are odd. Therefore, this puzzle is impossible. Remember: You can only solve a puzzle if it has TWO ODD NODES or NO ODD NODES.

In this drawing there are 2 odd nodes, which means that there is a solution. In the case of 2 odd nodes, you must always start on one odd node and stop on the other.

In this drawing there are no odd nodes, so this puzzle also has a solution. When there are no odd nodes, you will always stop at the same point you started on!

...You may wonder and ask, "What if there is only ONE ODD NODE?" The answer is that it is IMPOSSIBLE to draw a figure with only a single odd node, even by cheating!

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