3 Box One Continuous Line Puzzle Solution

1. The Five Room House Puzzle is a classic mind-bending puzzle and is called impossible by many. The puzzle is presented as a rectangle divided into five rooms. To solve this puzzle, you must draw a line through all five of the rooms walls while avoiding to go through the same wall twice. Though the puzzle looks simplistic to the eye, it gets very complex the more you think and try to solve it. So how do you solve the Five Room House puzzle?

Materials

• A piece of paper
• pencil/pen/marker
• (optional) printed copy of Five Room Puzzle

How to Solve

• The puzzle does not have a solution. Or at least, a "simple" solution. This can be said because of the Graph Theory. According to the graph theory, each room plays as a vertex and each wall is an edge. You can see how this is done in the image below.

• Even though it may look like the puzzle cannot be solved, it can. And to do that, you must think outside the box, literally. Some solutions are simple, others are more complex. These are some out-of-the-box solutions.

• Solution 1

• This solution uses a single curved line. It is one of the more simple and over thought solutions. This qualifies as a solution as it goes through each wall only once and visits all 5 rooms. Looking past the simplistic look, it cleverly finds a way to go through the puzzle quickly. This also took the advantage of using an abstract and curved line instead of straight angles.

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• Solution 2

• This solution is called the diamond because of its resemblance to the diamond shape. This solution is far more complex as you will grow to become more confused as the line continues and the shape becomes more complex. The diamond consists of multiple obtuse angles as they go in around rotation towards the center of the puzzle. In simpler terms you must start with the outside walls with long angles and work you way inside with smaller angles.

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• Solution/attempt 3
• This solution, or attempt, was created by me and is the most abstract and common of all solutions. As you can see each line in this corresponds with the other, this worked in a rotation, which cannot is the most efficient but it is not made to work at all times. Though this also contributes to a common strategy to the puzzle called "Inside-out." This was attempted by me before I had any knowledge of any strategies to this puzzle, as you can already see some flaws. The inside-out method is when you go inside the house, and once you go through the walls you exit through the other side. This is not necessary, the goal is to go through all walls in each of the five rooms. Most victims of the puzzle are fooled with this simplistic method, as it becomes their goal without them knowing it.

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• Conclusion
• By testing out ways to find a solution, you work on your mistakes, and build strategies to avoid those same mistakes. This puzzle is not just fun, in fact, you're it helps you with reasonable thinking, and associated with the term "think before you do." For example using the inside-out method was found to follow many mistakes in the puzzle. By avoiding that method you can think of more strategies . disclaimer: picture is simply made to point out flaws and improvement. May is not a correct solution.

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• In my case above, I found that using straight lines and angles, is easier to spot mistakes and is able to go through the puzzle more efficiently. Also abandoning the inside-out method gave me an advantage at the end of the puzzle. This puzzle is solved by deductive problem solving, as well as trial and error. Though there isn't an exact solution, this puzzle requires you to think outside of the box. The five-room house puzzle has many out-of-the-box solutions, but the one you get may as well depend on the way you think.

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Source: https://sites.google.com/site/hsawh2015ammar26/five-room-house-puzzle

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