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The Envelope Enigma

The Envelope Enigma

This weeks’s activity comes from the field of recreational mathematics. While the puzzle may not seem very mathematical (other than using mathematical language like points and line segments), it is actually related to the mathematical fields of network theory and topology. In this puzzle, students are asked to connect six points (labeled A-E) with line segments to form the outline of an envelope. To make this a challenge, students must do this without lifting their pencils once they start. In addition, they may not cross any lines already drawn or retrace any line segment.

Finding one of the multiple solutions to this puzzle is fairly easy using the trail-and-error method of problem solving. However, the puzzle is tricky enough that students are not likely to solve it unless they persist. This makes the puzzle an ideal one for starting out the new school year. To facilitate students’ problem-solving efforts, multiple sets of points are included on the student sheet. This allows students to keep trying until they come up with a solution. It also provides a way for students to label their solutions once they have solved the puzzle.

I hope that you find this activity, as well future Puzzle Corners, valuable for your class. If used consistently, they should foster an environment in which students find themselves enjoying math and developing essential problem-solving skills.

EnvelopeThe challenge in this puzzle is to connect six points (labeled A-F) with line segments. When connected, they should look like an envelope with its flap open, as shown. You must do this without lifting your pencil, crossing over any lines, or retracing any lines. Use the sets of points provided below to solve this challenge. After finding a solution (there are several) make a record of it. To do this, circle your starting point. Then add numbers and arrows to each line segment showing the order and direction in which they were drawn.



Click the arrow below to view the solution.

Envelope Solution

2 Responses to The Envelope Enigma

  1. It has to do with the even and odd vertices. Notice the start and end only have 3 segments that enter or leave the vertex, yet others have 2 or 4. This puzzle is a great way to start to notice patterns. You can continue with other networks and then develop your own conjectures about whether a puzzle can be traced without revisiting a line segment again.

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