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# A little game to relax your mind.

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Back in high school our science teacher gave us this puzzle...i still havn't figure it out. Simply draw a line through every "door" but you cannot go through the same one twice.

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Not exactly a science project or homework, but we can try and solve it scientifically.

Where do we start from?

1- Upper corners

2- Lower corners

3- Upper junctions

4- Lower junction

5- Mid row left/right junction

6- Middle row middle junction

Use all the possibilities. If you find none, then this is impossible.

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Are we sure it's possible? Each time you enter and leave a room, you have removed two doors. There are three rooms with five doors - this means that if you enter the room, and leave from a different door, then you must end up in that room, right?

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This could be solved if you took a sledge hammer and made another door to the outside from one of rooms with an odd number of doors :naughty:

I imagined putting a chair in each room and one outside, labeled the chairs A to thru F. Each time you enter a room or the outside sit in the chair. I made a simplified schematic with points A-F representing the chairs and connected them with lines representing each possible path thru a door and checked off the doors one by one. Then I made a table counting the number of lines at each point. A 4, B 5, C 4, D 5, E 5,F 9. Same thing. You can have no more than 2 points with an odd number of paths, start and finish. Every other point has to be an even number of connecting paths, pairs entering & leaving. Either that or form a closed loop and all the rooms have to have an even number of doors. Cool puzzle.

Can you use a hyperdimensional pencil?

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You will be forever trying to solve this one. It has been around at least 100 years. No one has solved it yet. Tens of Thousands and perhaps millions have tried this.

My Dad showed me this one when I was a kid. He learned it when he was a kid. I used to have fun with a few people who thought they were smart. This puzzle would stump them every time.:naughty:

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yes, this is definately impossible.

There is no possible way to finish this puzzle.

My math teacher told us he would give us an A plus for the entire semester if we ever solved this.

No one ever did. No one ever will.

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well that puts me at rest then! i thought it was incredibly sad that i could not figure it out for a few years...

to answer the first question, the only rules are go through every door only one time. start anywhere anyhow, just one time through every door.

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I've finally completed the list today. Tried every single possibility, (I think) and not found one way of doing it.

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lets try an dborrow that "hyperdimensional pencil" :)

it's a little embarassing how much time i have spent on this only to find out its impossible :hihi:

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This problem is analogous to the problem of Koenigsberg bridges, solved by Euler.

If you let each field and the area outside be points/vertices and doors be represented by lines/edges connecting these points, then you get a so called graph. Euler proved that in order for the graph to have the property described above, i.e. in order to be able to go through each door once, each point/vertex must have an even number of edges meeting in this vertex. Now, in our case we've got only 2 such vertices out of 6 ... and hence we can be sure it won't work.

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