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Linking Loops

Linking Loops

This week the Puzzle Corner activity utilizes concepts from one of the most recent fields in mathematics – topology. Topology is the study of geometric properties that are not affected by changes in size and shape. This includes the study of knots, inside and outside, networks, and the transformation of shapes and surfaces.

Linking Loops is a classic disentanglement puzzle that has been around for many years. If any of your students are familiar with it and know how to solve it, be sure to ask them not to give away the answer to their classmates.

Students will need to work in pairs for this activity. It is best if you pair boys with boys and girls with girls. Each student will need a piece of string about 150 cm long. The string should be at least the thickness of kite string. Students will tie a loop at both ends of their string through which they will slip their hands. These loops should fit loosely. Check to see that all students are properly connected to their partners, as shown in the diagram on the student sheet.

At first, this puzzle tends to be fairly difficult for students, and they will likely spend a lot of time going between legs and over heads in attempts to separate themselves. At some point, however, students should realize that no amount of acrobatics or contortions will separate them from their partners, and begin to think about the problem logically. You will probably need to spread this activity over the course of a week or more to give all pairs a chance to discover the solution for themselves. Encourage students who do discover the solution to keep it a secret so that each group can experience the satisfaction of solving the puzzle.

1Take your piece of string and tie a loop in each end so that your hand can fit easily through the loop, with room to spare.
2. Put your left hand through one of the loops.
3. Link your string with your partner’s string, and place your right hand through the remaining loop as illustrated.




Challenge: You and your partner should now be joined by your strings. The challenge in this puzzle is to detach yourself from your partner without cutting either string or removing your hands from the loops at any time. Good luck!



I hope you and your students have fun as you try to discover the solution to this topological challenge. In fact, you may want to bring a camera on the day that you assign this puzzle to capture some of the interesting and often humorous positions that students will get themselves into.


Click the arrow below to view the solution.


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