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Comment by ricardobeat | Hacker News Reader

I just solved that 9 dot problem in a minute with paper and pen. Maybe it was the chocolate I ate?

Just knowing that it's a hard problem can make you "think outside the box" (literally in this case). No electrocution needed. Could the results be a reflex of the participants' state of mind, not a direct effect of brain stimulation?

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My problem with the 9-dot problem is that it is culturally biased. If you grew up playing "connect the dots" as a kid, where you were trained over and over not to draw any lines that either strayed outside the figure or didn't connect to dots at both ends, you will probably find that puzzle very hard. If you didn't, you may not find it that difficult.

So if the transcranial stimulation experiment proved anything, it may have shown that the subjects didn't become more intelligent per se, but simply better at looking past their preconceptions.

Seems that no one can reproduce the study in question, so it's a moot point IMHO. Just snake oil, and/or typical psych researchers who made a 'C' in statistics.

There is a solution that requires you to use a semicircle line to join two of the straight lines. You could argue it meets the rule 'just four straight lines', and you would be all the more 'creative' for proposing it. However it is unlikely to be suggested because the convention is to draw lines that directly connect dots.

If you make the lines long enough, and take it literally as connecting dots as opposed to points, you can do it with three: Connect the three top (or whichever side) and extend that line out far enough that you can then draw a diagonal line that slopes slowly enough to be able to connect the dots in the next row, and repeat for the last row.

But I spent far longer than I "should" have, because I wrongfully just assumed no crossing lines - another common convention that was never stated but that just was too hard to ignore. I did try various diagonals trying to get to something similar to the linked solution before the "three long lines" approach, but didn't get there because of getting stuck on that.

I think a lot of the time the bigger problem than getting "creative" is to clear your head of all the unstated assumptions that are very easy to cling to without even realizing. A useful method can be to try solve a problem with fewer restrictions, and then add restrictions back in and see what solutions can be adapted - that makes it harder to get stuck considering rules that don't actually exist.

I nearly punched out my monitor when I saw the "solution".

By that metric I count my first solution of "Cut the image up into a straight line and connect the dots." as valid.

EDIT: I agree about state of mind, the reason I would say nobody could "solve" that problem was their mental model of the parameters of the problem wildly diverged from the authors.

I've seen worse. Here it is in 3 lines :) http://www.jimloy.com/puzz/9dots1.gif

There's a variant of this riddle where the solution is using a big brush and painting over the dots in one stroke.

I think all of these solutions are interesting and creative.

Yeah, that was my solution. Only when told they were points, not dots did I find the four line one.

You can also do it in one, if you imagine the line to lie on the surface of the earth and to wrap around the entire earth three times.

The solution doesn't violate or bend the guidelines given (using four straight lines). Assuming that some strict rules exist seems to be a cultural behavior - probably ingrained from school, where doing things creatively can get you in trouble. </sociologist>

On the other hand, if you have seen these kind of problem before, you already have a hint that the solution involves something unusual.

> The solution doesn't violate or bend the guidelines given (using four straight lines).

Yeah; which is partially my frustration. The other part is that I actually went pretty in depth compared to how much time I would expect most people to go at it. (About an hour with a pencil and paper journal. Figuring out what couldn't be the solution with "You're starting from one of the dots" as an implicit axiom.) I was actually about to write a script to brute force the solution after I ran out of ideas, until I decided to save myself the time and peek at the solution.

I think you can imagine how that turned out.

Actually it's quite easy to bruteforce by hand if you mention that point set has multiple symmetries. For example, you only need to start drawing lines from (0,0), (0,1) and (1,1). Any other combinations are derived by rotation and mirroring. After several minutes you can prove that solution in impossible under implicit presumption that every line must terminate at a dot. And after that puzzle is really easy.

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