Is there any solution for this puzzle?

Question

There is a house with 5 room and one door with every single wall as shown in following figure. You have to visit every door exactly once but there is a condition that you cannot cross the path.

enter image description here

I tried hard to get a path but i failed. Is there any solution exist ??

No, sadly there is not. Here you can find out why: Click me! — Cristian Marian, Jul 01 '15 at 15:04

Curmudgeon · Answer 1 · 2015-07-01T15:29:42.240

3

Assuming you can't walk through walls, you can only cross through a given door one time, and you have to cross through a door to "visit" it, this is impossible. Because...

enter image description here

Rooms 1, 2, and 4 have odd numbers of doors. Logically, if a room has an odd number of doors with our rules, if you start outside the room, you must end inside the room. Similarly, if you start inside the room, you must end outside of it. Draw some lines and you'll see what I mean -- no matter what, for each time you enter a room, you must leave it unless you are ending in that room.

Here's an image demonstrating this (left - start in, end out; right - start out, end in)

enter image description here

Because there are three different rooms that have odd numbers of doors, no matter where you start you logically need to end in multiple rooms to be able to solve the puzzle, making it impossible.

edited Jul 01 '15 at 15:29

answered Jul 01 '15 at 15:10

Curmudgeon

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just read up on this on this page: https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg. there can only be zero or one odd-vertex nodes in the whole map for it to be traversable. this map has three odd nodes. – dfperry Jul 01 '15 at 15:13
@dperry zero or two, surely? – frodoskywalker Jul 01 '15 at 15:25
yes, typing without thinking again – dfperry Jul 01 '15 at 15:26
A graph with one odd-vertex node is also traversable, if you are sufficiently patient. – Anon Jul 01 '15 at 15:38
@Anon I am intrigued, please give an example of a traversable graph with a single odd-vertex node. – Taemyr Jul 02 '15 at 13:04

score 1 · Answer 2 · answered Jul 01 '15 at 15:06

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I don't think this is possible!

for every room, there should be an even number of doors in order to get in and out without crossing ( you have to get in through one door and out through the other). Which is not the case here!

answered Jul 01 '15 at 15:06

Mohammad

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There could be one or two rooms with odd numbers of doors -- if there was just one, it's easily solvable so long as you start or end in the odd room, if there are two, you must start in one of the odd rooms and end in the other one. – Curmudgeon Jul 01 '15 at 15:24

Is there any solution for this puzzle?

2 Answers2