by Dave Youngs
This month’s Puzzle Corner activity is a modification of a classic puzzle from recreational mathematics. This classic puzzle appeared in AIMS® (Volume VI, number 10) and the AIMS book, Puzzle Play. As mentioned in those publications, the idea for the puzzle came from Martin Gardner’s column in the November 1978 issue of Scientific American. Gardner traced the origin of the original puzzle, which came to be called a hypersquare, to an entrance exam from the school of architecture at the University of Leningrad.
Both the original puzzle, which was called Cut and Fold Challenge in its AIMS’ versions, and the adaptation presented here, Cut and Fold Challenge II, are difficult puzzles for those who do not possess strong spatial visualization skills. However, with some persistence and a lot of trial and error, those who invest the time can solve these puzzles. I strongly urge you to try this puzzle before assigning it to your students. This will accomplish two things. First, it will give you a good idea of what your students will face as they work on the puzzle, and second, it will provide you with a three-dimensional model to share with students. (The flat base of this 3-D model should be taped to another piece of paper so that students can’t untwist it—doing so gives the solution away and robs them of the chance to experience the joy of discovery.) To introduce this puzzle to your students, you can either distribute copies of the student sheet and have them follow the directions on it, or show students the 3-D model you’ve created and challenge them to replicate it. You’ll need lots of paper for this activity—copy paper cut into eighths works well.
As with any Puzzle Corner activity, students should be encouraged not to share their solutions until all have had ample time to work on the puzzle. My practice was to introduce the puzzle on a Monday and then allow students to work on it during the week. If they solved the puzzle during that time, I had them tape their solution to another sheet of paper and pin it to the bulletin board. On Friday, I set aside time during the math period for students to share their approaches and solutions to the puzzle.
I hope you and your students enjoy this activity.