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Appropriate cheating in the nine-dot problem

All geeks, nerds and puzzle folks are aware of the nine-dot problem, along with the lesson it is frequently used to present.

NinedotHere's a pencil. Here's a piece of copy paper with nine dots on it. Without lifting the pencil or folding the paper, connect the nine dots using four straight lines.

The narrator smiles as you try as hard as you can, unable to do it. Then he ends your frustration and points out you've been tricked by your own limits, because, of course, there's nothing in the rules that says you can't have the lines go beyond the edges of the nine dots.

The thing is, this isn't the end. This is the beginning of the cheating, and anyone who stops here, satisfied at his breakthrough, is missing the point.

Some innovators point out that because the dots and the pencil have width, it can actually be done with three lines. (Here's how). At this point, some people get uncomfortable because a lot of what we assumed (the edges of the nine dots, their magical zero width) is being challenged.

I think we can go far beyond this.

What revolutions do is change more than a few common conceptions. If you roll the paper into a tube, with the dots on the outside, you can go round and round and round (like an Edison music cylinder) and do the entire thing with just one line. Without folding the paper.

That's cheating! (You could also burn the paper and just call it a day at zero)...

Wikipedia is that sort of solution. So, in fact, are just about all of the innovative successes of the last decade. They took an assumed rule and threw it out. People who have been online for awhile have seen this happen over and over, and yet hesitate to do it with their own problem. Not because it can't be done, but because it's not in the instructions. And the things we fear to initiate are always not in the instructions.

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