by Dave Youngs.
Puzzle Corner | Student Activity Page
This month's Puzzle Corner activity is based on a thought problem from recreational mathematics that most people find difficult. (I remember puzzling over it for quite some time before coming up with the solution.) In this problem, people are challenged to think of a way to support a pot over a fire using only four metal strips and four rocks evenly spaced around the fire. This seems like a simple thing to do, but there is a hitch - the rocks can't be moved and they are too far apart for the metal strips to span the gaps between them. If you've not encountered this brainteaser, think of how you might solve it.
Although the original thought problem is quite difficult, even for adults, it can be adapted for use in upper elementary and middle school classrooms if two things are done:
- materials are provided so that students can actually build the structure necessary to solve the thought problem, and
- students are allowed to build a number of other supporting structures before being given the challenge of the original brainteaser.
While a variety of materials can be used to model this brainteaser, the ones chosen here are paper cups and craft sticks. Each student or group working on the problem will need four craft sticks and five paper cups. The craft sticks represent the metal strips of the original problem. The rocks are represented by four of the cups placed upside down on a flat surface. The fifth cup, placed right side up, represents the pot.
To get students used to building with these materials, they are given a warm-up assignment in which they are asked to construct various structures using only the craft sticks and four cups to support a fifth cup. Since there are no restrictions in this warm-up activity, students should be able to quickly build several workable supporting structures. Placing the four cups close to each other and placing the craft sticks in a tic-tac-toe-like arrangement on the cups can make one such structure. This provides a sturdy platform for support the fifth cup. There are a number of other similar structures that can be built quite easily. Students should be given enough time to build several structures and sketch them in the space provide on the student sheet before moving on to the challenge.
After this initial construction experience, students are ready to tackle the harder problem posted by the original brainteaser. In this challenge students are told that they must now try to build a structure in which each craft stick only touches one supporting cup. In other words, the craft sticks can't be used to bridge the gaps between the cups. After some failed attempts, students may claim this is impossible without using some additional materials, like tape or glue, to connect the craft sticks to each other. If this happens, you will need to assure students that this task is possible.
If you sense that this puzzle may be too frustrating for you students, you may want to do it as a group, rather than individual activity. Another option is to let individual students work on the puzzle for a set period of time in class, and then encourage them to take the cups and craft sticks home so that they can work on the puzzle over a longer period of time. Many veteran puzzle-solvers know that it is sometimes helpful to put a puzzle away for awhile and then pick it up again at a later time. These puzzlers often find that the solution comes easily on subsequent attempt.
I have that you and your students enjoy this puzzle.