Five screw-puzzles by George Hart

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These five puzzles require creative thinking to combine translation and rotation transformations in innovative ways. In math class, they spark inspiration by showcasing mathematics as a fun and engaging field with numerous applications. As students progress through the challenges, they become comfortable with exploring unknown problems, which is an essential skill. The set of puzzles encourages problem-solving strategies and yields a satisfying "Aha!" moment when the final solution is discovered, promoting a sense of enjoyment in mathematics. Two-part bagel: This puzzle is straightforward but sparks curiosity to replicate it by cutting a real bagel. Students are naturally led to understand the geometric form to solve the next challenge. Four-part torus: This shape is slightly more challenging, offering two approaches: solving it piece by piece or combining pairs of pieces for a divide-and-conquer solution. Students can also replicate it by cutting a real bagel. Six-part torus: The logical progression from the previous puzzle, this challenge requires advanced students to prove that any sequence of assembly can solve the six parts, such as labeling them ABCDEF and solving them in various permutations. Four-part cube: These four identical pieces assemble into a cube without force required. Students can solve it incrementally or use a divide-and-conquer approach by first making two sub-assemblies. Two-part tetrahedron: The most challenging puzzle, despite having only two identical pieces, requires no force to assemble. It may take more than 30 minutes to solve, but the process encourages creative thinking and problem-solving strategies.