Solve the Strange House Puzzle - One Doorway Left!

  • Context: High School 
  • Thread starter Thread starter M12
  • Start date Start date
  • Tags Tags
    Strange
Click For Summary

Discussion Overview

The discussion revolves around a puzzle involving a strange house layout with five rooms, each having doorways on every wall. Participants are tasked with finding a continuous path that passes through every doorway exactly once, exploring the feasibility of such a path.

Discussion Character

  • Exploratory, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses frustration in finding a solution, stating that they have tried almost every possible way without success.
  • Another participant agrees, indicating that they have also attempted various paths but conclude that one doorway always remains unvisited.
  • A later reply draws a parallel to the Bridges of Königsberg problem, suggesting that the existence of an Eulerian path depends on the number of vertices with odd degrees, noting that three vertices of odd degree would imply no Eulerian path exists.

Areas of Agreement / Disagreement

Participants generally agree on the difficulty of the puzzle, with multiple views on its relation to known mathematical problems, but no consensus on a solution exists.

Contextual Notes

Participants reference the properties of Eulerian paths and the implications of odd degree vertices, but the specific configurations of the house and doorways are not fully analyzed or resolved.

M12
Messages
1
Reaction score
0
Imagine that the picture shown below is an overhead view of the layout of five rooms in a very strange house. The reason that this house is so strange is that every room has a doorway on every single wall. Your task is to find a continuous path that passes through every doorway exactly once.

http://img258.imageshack.us/img258/5387/3dhouse.th.jpg

The image below is an example of an unsuccessful attempt to solve this problem. The path shown in the diagram passes through every doorway except for one. There is no way to reach the final doorway without passing through one of the doorways twice!

http://img516.imageshack.us/img516/558/exampley.th.jpg

Hint: To make it easier, just copy - paste the image onto paint, erase the previous blue lines, and have fun figuring it out!

P.S. If you do figure this out, please share! I've tried almost every possible way and I still can't figure it out. Thanks!
 
Last edited by a moderator:
Mathematics news on Phys.org
Well,
suppose there is a path.
Each room with an odd number of doors has to be the start or the end of the path.
But there are 3 rooms like that.
So it is impossible.
:smile:
 
Last edited:
yup.. tried all ways.. even intersected paths... it is impossible because 1 doorway always remains...
 
Seems similar to the bridges of konigsburg problem. A graph has an Eulerian path iff the there exist precisely two vertices of odd degree. Three vertices of odd degree <=> no Eurlerian path.
 

Similar threads

Undergrad Can Mathematical Sharpness Puzzles Challenge Your Problem-Solving Skills?
  • · Replies 13 ·
Replies
13
Views
4K
High School Can high voltage static electricity cause a shock through a power cord?
  • · Replies 6 ·
Replies
6
Views
3K
High School Can we say a photon doesn't exist until the wavefunction collapses?
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Who Lives Where? A Logic Puzzle with Neighbors and Clues!
  • · Replies 21 ·
Replies
21
Views
7K
High School Infrared Detectors & The 2nd Law of Thermodynamics
  • · Replies 152 ·
6
Replies
152
Views
11K
Graduate Homemade Quantum Eraser Experiment revisited with photos and full text
  • · Replies 13 ·
Replies
13
Views
8K
PF Fan Fiction: Mathematicians in Love
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Some questions about Cosmic Microwave Background radiation
  • · Replies 13 ·
Replies
13
Views
7K
How to stop a weight from falling
  • · Replies 27 ·
Replies
27
Views
5K
Graduate Solve the Small Problem: A Puzzle Challenge
  • · Replies 9 ·
Replies
9
Views
3K