by Dave and Michelle Youngs
Before reading about this month's puzzle, try the following warm-up challenge. If you are already familiar with its solution, read on. If not, please take a few minutes right now to solve it.
On a piece of paper, draw nine dots as shown below. The challenge is to connect each of the dots with four straight lines. Each dot must be crossed once, but not more than once, and you cannot lift your pencil from the paper once you have started.
The type of thinking required by this problem is very similar to that which students must use to solve Column Changing Challenge. There are several solutions to the challenge above, but each requires you to extend the lines beyond the arrangement of dots. In fact, some believe that this puzzle is a possible origin of the phrase "thinking beyond the box," which has come to be synonymous with creative and divergent thinking. Although the directions say nothing of the kind, we tend to approach this problem, and others like it, with a notion that you should not be allowed to go beyond the arrangement of dots to solve the puzzle. This kind of thinking boxes us in and contributes to making the fairly simple solution so difficult for many to discover.
Column Changing Challenge is another problem which requires students to think beyond the box. At first glance, the problem seems impossible, and indeed it is when approached from the angle that most people initially take. However, with a little persistence and divergent thinking, the answer becomes clear and seems quite simple to those who have discovered it.
In this puzzle two distinct manipulatives are arranged in four rows of four so that they alternate like a checkerboard. We have suggested pennies and nickels, but any other small manipulatives of two distinct types or colors will work equally well. The challenge is to move two of the coins so that the resulting arrangement is no longer checkered, but consists of alternating columns of all pennies and all nickels. For example, the far left column would be all pennies, the next column all nickels, the next all pennies, and so on.
I hope you and your students use this puzzle as an opportunity to think beyond the box and stretch your creative and divergent thinking skills. If you have questions about this, or any other Puzzle Corner activity, feel free to contact us at AIMS. P.O. Box 8120. Fresno, CA 93747.