Nine Magic Dots and R&D : Page 2 of 2
Nine Magic Dots and R&D
A HABIT THAT SPOILS R&D CREATIVE THINKING: We use restricted definitions that limit our mind funnels and our creative thinking. We stay stuck in old paradigms.
With expanded boundaries, clarified assumptions, and unrestricted definitions, we can solve the 9 dot, 3 line problem in this way:
Go off the paper, if necessary
Go off the paper, if necessary
The first line touches the side of the first dot tangentially, passes through the center of the second dot, and touches the side of the third dot tangentially. Extend the line as far as necessary, even off the paper, so the second line can do the same to the middle row of dots, and similarly for the last line and the third row of dots.
There's another solution based on non-Euclidean geometry which postulates that parallel lines meet at infinity. Using this mind funnel, the answer consists of three parallel lines, each of which touches a different row of dots, and then all three lines connect at infinity, a neat paradigm shift.
A True Story: In a creative thinking workshop, one participant said she discovered this solution based on non-Euclidean geometry, but discarded it because she thought it unfair. This solution lay outside her comfort zone.
A HABIT THAT SPOILS R&D CREATIVE THINKING: We only express 'fair' ideas, even before we select one. Don't let fairness spoil creative thinking in your head.
Here's another forced-withdrawal with the same nine magic dots.
The problem: Use two connecting straight lines that touch each dot only once.
Think it impossible? Check your assumed boundaries, unwarranted assumptions, unstated criteria, restricted definitions, mind funnels, and paradigms.
One block to this problem lies in your restricted definition of a line. In school, teachers define a line as a series of connected points that have only one dimension, length. In real life, lines have width. Look at traffic lines in the center of the road or lines of buses approaching an intersection. Again your habit of restricting definitions blocks you and led to the unwarranted assumption that you could use only thin lines.
Here's one answer to the 9 dot, 2 line problem: A wide line and a narrow line!
Try one last forced-withdrawal with the same nine magic dots.
This time use only one straight line that touches them all. Find at least 15 answers before you continue reading.
Actually hundreds of acceptable solutions exist. The few solutions here will trigger new paradigms and mind funnels, and whet your appetite for more.
In my workshops on creative thinking, I always hear new and different solutions from the participants. See how many new solutions you can discover. Send me some. I always enjoy more.
Nine Magic Dot can help the creative climate of your mind.
You should realize by now that this puzzle represents a metaphor for problems at work. You can learn a lot from these nine magic dots. •
Excerpted from the R&D Creativity & Innovation Handbook, © 2011 by Edward Glassman. All rights reserved.
Edward Glassman, PhD was the President of the Creativity College®, a division of Leadership Consulting Services, Inc., and Professor Emeritus of the University of North Carolina at Chapel Hill, where he headed the Program For Team Effectiveness And Creativity. More »