Solving a 1000-Piece Jigsaw Puzzle Maze

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SUMMARY

This discussion explores the concept of creating a jigsaw puzzle that functions as a maze with a single entrance and exit, solvable in two distinct configurations. The proposed design includes a "dead path" that is not connected to the start or exit, surrounded by a wall. The puzzle consists of 1000 pieces, including edge pieces, with two uniquely shaped pieces that can be swapped to alter the solution. This innovative approach challenges traditional puzzle-solving methods by introducing a dynamic element that affects the outcome based on piece placement.

PREREQUISITES
  • Understanding of jigsaw puzzle mechanics
  • Basic knowledge of maze design principles
  • Familiarity with combinatorial problem-solving
  • Experience in puzzle creation or design
NEXT STEPS
  • Research techniques for designing solvable mazes
  • Explore jigsaw puzzle manufacturing processes
  • Investigate combinatorial game theory
  • Learn about piece interchangeability in puzzle design
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Puzzle designers, game developers, educators in mathematics, and enthusiasts interested in innovative puzzle mechanics will benefit from this discussion.

dariusmartin
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A few days ago I was watching a youtube video of someone solving a jigsaw puzzle and a thought came to my head; is it possible to make a maze with only one entrance and only one exit that is printed out on a jigsaw puzzle, where the only way the maze is traversable is if the puzzle is solved in 1 of 2 different configurations? (1000 pieces including edges)
 
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I think so. Make a maze with one solution and with one path (call it the "dead path") that is not connected to the start or exit and with a wall on the boundary of the puzzle. Then determine a jigsaw puzzle for it. Now, cut out a uniquely shaped piece at the exit and an identically shaped piece on the exterior boundary of the dead path. Those two pieces should be swappable. With the two pieces in their original positions, there is a solution. With the two pieces swapped, the exit is blocked and the prior exit is now moved to an exit of the dead path that does not connect to the start.
 
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