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Outside the box
Think outside, but not too outside...
By: David K. Every
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2002-03-11 07:48:06
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 here's a standard test, where 9 dots are a places on a page, and you're told to connect all the dots without lifting a pencil off the paper, in the fewest straight lines as possible.
When you first look at the problem, the answer seems like 5 is the fewest number. But the tester usually tells you that it can be solved in 4 lines. Then they go away and leave you to ponder this conundrum for a while, and return to give you their smug answer.
The answer they are looking for is as follows:
Then the tester tells you that since you were thinking "inside the box", you couldn't solve the problem.
I was a little different. When I was given that test, I looked at it for a few seconds and said, "heck, I can to it in 3 lines, or 3 ways to do it in 1 line". Which befuddled the tester, since the obvious proper answer was the one he was told which was 4 lines. How could I do it in 3 lines, or 1 line?
Three lines is easy... just make them long lines in a big Z.
They are dots, not points - so they aren't infinitely thin (nor is the pencil). That was easy -- but he sort of felt it was cheating (even though I was conforming to all the rules set before me). But then he really wasn't going to like my other three answers.
The first was simple. Split the pencil in half (lengthwise) and then use the exposed lead to smear one really big-fat line across all dots in one swipe.
The next one was to stop thinking in two dimensions. Wrap the paper in a cylinder (with the dots on the outside), and then like an old phonograph, draw one straight line along the outside surface, in a slowly discending direction, that would eventually bisect all the dots. It doesn't matter how many revolutions it takes, it will eventually cross all the dots, and I'll never have lifted the pencil.
The third way was a variation on the last. Just fold the paper up so all the dots are aligned over each other, then place the pencil on the first dot and push it through the paper (in one line). This third dimensional line will go through all the dots (literally). Or if your in a less destructive mood, you can just fold it so the edge of the dots are on the edge of the page (but lined up) and draw across the edges. I didn't even get into the other more bizarre ways that shot through my mind which usually had cutting, tearing or folding the paper to allow one line to bisected all the dots.
The tester didn't like my answers. It seems that I thought too far outside the box. Ironically, the way I didn't think of solving the problem was the one he was looking for - which is with four lines.
       
The point is that the way to think outside the box was not only to question the solution but to question the problem or tools themselves. If the problem was to get black "lead" on all the dots, then use a fatter line, or fold/manipulate the paper/dots to make the problem easier.
If you question to tools and the problem itself, you can come up with more creative ways to address them and truly be thinking outside the box. However, such extreme solutions while being technically correct and solving the problems, will annoy those who might want to think that they think outside the box, but are only disturbed by those who really do. 
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