Dot Puzzle

What is the Nine dots puzzle?
The goal: Connect the nine dots with four connected straight lines without lifting your pencil from the paper. You can start from any point.

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The puzzle was originally used by the Gestalt psychologists who believed that problem solving came in a brief moment of insight. These "insight-problems" were popular in studying the "aha! moment". Karl Duncker, the German Gestalt psychologist was the first to publish an insight study in 1926. He believed that there had to be one concise moment in where a solution just appeared. He designed twenty puzzles which he claimed could not be tested by reasoning. He had the subjects talk through the problem as they tried to solve it. From this information, he was able to identify several stages. Although his research was thorough, it was not able to pinpoint what exactly was going on.

Later research was able to contradict many Gestalt beliefsā€¦

  • 1. We're blocked from creativity by our past experiences and our unwarranted assumptions.
  • 2.When you break out of your fixation, the solution should come quickly and easily in a spark of insight.
  • 3.Insight solutions are independent to prior knowledge.

Research would eventually show that insight occurs over time and that the "Aha! moment" is really a myth. Kenneth Bowers, et al., designed a study which demonstrates how your brain works to come up with a solution. First, a target word is chosen. Fifteen remote associates of the word were chosen and compiled into a list. The subject, in reading through the list, would try to come up with the target word. Results show that individuals had an idea of what the word was after ten words and were confident after twelve. Subjects were asked to write a guess after every word. Analysis showed that there was a linear progression towards the correct solution- even before the individual was aware.

The solution
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Why did we use it?

The solution to this problem requires that you "think out of the box" in order to solve it. Your pencil must actually go outside the square of dots. Individuals typically struggle with this problem because it is not apparent that they must move the pencil beyond the range of the dots. The solution requires creative insight.

Why is this concept so difficult?

  • "There is nothing outside the square of dots to associate to. There are no dots to join a line to outside the puzzle so we assume a boundary exists.
  • We assume that drawing outside the dots is outside the scope of the problem, even though the problem definition doesn't say it is.
  • We feel so close to solving it that we keep trying the same way, but harder. "

In order to save space, we didn't upload the images from all of the plates. Only a handful of the students were able to solve the puzzle. Most left it blank. A few attempted the puzzle and failed.

Out of the 28 plates we recieved back, only one had a "different" solution.
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This person drew four lines that crossed the front and back of the plate. A VERY creative solution to the problem.

http://www.brainstorming.co.uk/puzzles/ninedots.html

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