Nine-dot problem

An example of a classic insight problem is the nine-dot problem. In short, the problem is to take a 3x3 square of dots, and draw four lines that connect every dot without picking up the pencil. In order to solve the puzzle, the person must reahze that the solution is to extend one of the fines beyond the confines of the box, and make a non-dot turn. This reconceptualization of the problem is rare, the subject cannot gauge his or her own progress, and continuous effort is usually not as helpful as taking breaks. 

Research on the nine-dot problem has shown that training on certain ideas such as non-dot turns in similar problems produces an increased success rate in solving the problem (Kershaw Ohlsson, 2001 Kershaw, 2004). This effectively mirrors the way axioms function in mathematical problem-solving—by increasing the number of axioms available to the subject, experimenters were able to greatly reduce the difficulty of the nine-dot problem for participants. 

Kershaw, T. C. (2004). Key actions in insight problems Further evidence for the importance of non-dot turns in the nine-dot problem. In Proceedings of the twenty-sixth annual conference of the cognitive science society (pp. 678-683). Available from http //www.cogsci.northwestern.edu/cogsci2004/papers/ paperl56.pdf... 

Figure 4.7 Nine dots problem proposed by Scheerer (4). Connect all of the dots by four straight lines without lifting the pencil from the paper. The solution is shown in Figure 4.8.

Figure 4.8 The solution to nine dots problem. (Source Reference 4.)...

Martin Scheerer (4) published several illustrations to exemplify how insight to a problem solution can he delayed or thwarted by fixation of an inappropriate solution. One example required that nine dots (Figure 4.7) he connected by four straight lines without lifting the pencil from the paper. To solve this problem, one must extend the lines beyond the dots (see the solution, Figure 4.8). Most people assume incorrectly that they may not do this and are not able to solve the problem. 

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See also in sourсe #XX -- [ ]

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