Nine point problem
The nine-point problem is a task from the field of practical problem-solving in thought psychology . The task is to connect 9 points arranged in a square with a pen with four or four or less straight lines without removing the pen. The problem was first described in Samuel Loyd's Cyclopedia of Puzzles in 1914.
The approach of test persons to this problem was investigated in experiments. Test subjects often take a long time to find a solution to the problem. This is because they tend to put additional restrictions on solving problems. For example, they often try not to leave the square when drawing the lines. The Gestalt laws can explain that. Only when this restriction is abandoned is it possible to solve the problem by drawing beyond the square. The thinking outside the box is thus a good example for the English term thinking outside the box (in German as: outside the prescribed limits think ) or commonly used in German About look outside the box , which plays an important role in the area of problem solving.
If the elements of the problem are not understood as elements of Euclidean geometry, solutions with less than four lines up to single line solutions are possible. For example, a solution in which a pen is selected whose line width is at least as large as the distance between the corner points, which each form an edge of the square formed by the points. Solutions that have something to do with spatial imagination are also given. One example is to set up the paper as a cylinder so that the nine points are arranged at an angle. If you drive around with a pencil, you get a spiral shape that connects the points. If you put the paper down normally again, you will see three parallel straight lines that are not perpendicular to the edge of the sheet. Children often find such solutions without major problems, since they experience the dots as small circles or lines with a line width.
Trivia
The Klaus Tschira Foundation uses the solution to the nine-point problem as a logo.
See also
Individual evidence
- ↑ Rainer Maderthaner: Psychologie , p. 250, ISBN 3-8252-2772-3 ( preview in Google book search)
- ↑ a b Willy Desaeyere: Think tank , ACCO Leuven 1998, ISBN 90-334-4051-2 , p. 101ff. (English, preview in Google Book Search)
- ↑ Sam Loyd: Sam Loyd's Cyclopedia of 5000 Puzzles, Tricks, and Conundrums With Answers . 1914, p. 301, 380 ( archive.org [accessed November 13, 2017]).
- ↑ Daniela Georgieva & Kristina Radzeviciute: Human Problem Solving (2007) (PDF; 98 kB)
- ^ Frederick H. Kanfer, Hans Reinecker, Dieter Schmelzer: Self-Management Therapy - A Textbook for Clinical Practice , Springer Verlag, 2006, ISBN 3-540-29961-0 . P. 50 ( Preview in Google Book Search)