Impossible Brain Teaser?

[Durro]

I've got the answer to the "impossible" brain teaser.

 

The solution involved putting a line through one of the circles, and not just touching it. Now, if I can only work out how to attach the image from my computer...

 

Hey, this is only my 2nd post, so be kind.

 

 

Durro

 

P.S. Hey, you can just attach images here ! Woo-hoo. That makes life easier. Here it is.

[Rhapsody]

so far as i see, timo has been the closest, if you set the houses and utilities as shown, and add the 3rd house at the top of a pyramid (hidden behind his/her middle utility on the sketch) then you have a straight pipe up the middle to the house on the peak, and a straight pipe up the edges from the other 2 utilities. in this way, all 3 utilities can even remain on the same plane

Edited February 8, 2011 by Rhapsody

[soundoflight]

When something ‘appears’ on the “surface” to be impossible either we need to alter our relative view of the “picture” or pay closer attention to the words that “frame” the “teaser”

 

“"Three houses need a gas line, water line, and electricity line, and all must be on the same plane underground."

 

 

 

 

What I see “reflected” in the question ( as to the progenitors' mindset) is selectively found within key words he/she used.

 

The first word that ‘appears” to be relevant is the word “plane”. As an extension: The "implied" meaning of the fuller expression ...“on the same plane.”

 

Definition of the word plane: “a plane is any flat, two-dimensional surface. A plane is the two dimensional analogue of a point (zero-dimensions), a line (one-dimension) and a space (three-dimensions). Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.

 

Thus the key(?) to this seemingly impossible inquiry is related to that which can alter the impossibility of something. From impossible to... possible?

 

Refer to the accompanying picture.This represents a 3-dimensional framing of the inquiry.

 

The vertical “square” marked '1' represents the houses as well as the “lines” running to the perspective “utilities.”. The “horizontal” “squares” ( marked 2&3) represent a “surface plane of reflection.” Number '1' is produced relative to the “plane” or screen ( its seeming vertical rise is illusionary). 2&3 represent a plane of reflection receiving light photon. ( this plane of reflection relative to light photon is what results in the “emergent“ geometry ) . This means that “square 1”( houses and utility lines) is “produced” ( projected) due to “a” plane of reflection and refraction of light. The combination of surface reflection and thickness refraction ( of plane) results in the 3D ( “emergent geometry) of “square 1.” As well this “combination” results in the illusion of the rising from the plane surface of the emergent geometries. ( house with utility “lines.”).

 

Note: All of this is actually occurring on a 1 dimensional..“screen.”

 

Light photon is being reflected upon and refracted into a 1 dimensional plane with 2 dimensional properties. The resultant geometry is a “holographic” (s)(3D= reflection combined with refraction.. of light) representation ( 3D picture or “video”) of what is happening on the surface of the screen and what occurs through the thickness. This holographic representation creates the illusion of depth ..or: The seeming vertical rising of the emergent geometry 'off of' or 'up from'...the screen.

 

What is happening with “square1” ( "seeming vertical" as opposed to number.. 2&3=horizontal) is actually occurring on the surface of the reflective plane. Thus what is happening with “square 1” is actually a product of the whole system ( whole picture ) (where light photon as necessarily reflected/ refracted is ..inferred).

 

That is to say: Light is being reflected to a surface of a reflective plane and then 'its' light is subsequently ( instantaneously) refracted into the reflective/refractive medium. This reflection/refraction of light photon is what results in the “emergent” ( seemingly vertical and 3 dimentionalized) geometry seeming to be elevated above the system ( rising vertical relative to the horizon-tal plane). However “square1” is actually occurring ( emerging) on the surface of the plane. The houses and utility lines are actually 1- dimensional HORIZONTAL geometries that, due to refraction, are appearing to be 3 dimensional.

 

Note: “No doubt”… this is the reason why the author of the “brain teaser” ( more appropriately “eye teaser,” drew the lines from the houses as if they are rising above the houses verses representing the (utility) ‘lines” running horizontal to the vertical houses).

 

Thus 2& 3 represent both 'surface reflection' as well represents the thickness of the plane. As “square 1” is illusionary( as seeming vertical)…so is “square 4” equally as illusionary( as seeming vertical). Thus 2& 3 represent both the surface of the medium( relative to light and sound) and the furthest point away from the surface as representing the thickness of the medium.... as well the “actual” part of the medium that reflects the light back to the surface.

 

Imagine that you lay a mirror down horizontal and place a cube on the mirror. The cube will reflect downward into the mirror. Yet we are aware that the “dual image cube” is actually occurring on the surface. Thus the “dual 3D image cube” …”down into” the mirror is actually occurring on the 1D surface of the mirror. Thus:

 

... “square 4” which simulates ( dual symmetry reflected… as well technically; refracted) the depth of the “ground” is actually occurring on the surface. Thus “square 4” represents deep down into the ground where “one set” of utilities would run from “one emergent geometry …(house).

 

.. “square 2” represents another reflection along the horizontal surface ( back). Since “square 2” is representative of surface reflection as well as : “true thickness refraction” ( one way) then part of its thickness represents “down into the ground.” Thus another one of the utility lines from another house would be running under ground this way. The same would prove true relative to:

 

“square 3.”

 

Thus as you see ..if we remove from the equation the “real emergent geometry’ ( “square 1”) then what would be remaining is 3 parts of the whole system( consisting of 4 parts) ... that are equally efficient in providing a means of running the utility lines so that they do not ‘cross each other or.. under or over the others.’

 

As you will see “square 4” is centered between “squares 2& 3' and in the strictest sense these utility lines( from "square 4') DO NOT run over or under “squares 2&3.”. As well you will notice that:

 

from square 1 to square 2 represents ‘3 utility lines.’( left)

 

From square 1 to square 3 represents ‘3 utility lines’ running from the center( square 1”) to the right.

 

As well ’three utility lines’ are running from square 1 to square 4( downward).

 

Thus ’9 utility lines’ running from 1 “emergent geometry” ( 3 houses) that do not ’cross each other’ or “run under or over the others. ( reiterate: “square 1' is.. NOT.. part of the equation.)

 

 

Now take this picture into a paint format..and I will show you the “inverted relevance” of the whole system. A system that shows the relationship between light photon and reflective/refractive planes.

 

Explanation ( holographic effect) ( AFTER inverting the colors of the whoe picture)

 

If you “high - light” the whole picture and invert the image you will see 3 houses sitting upon acreage( surface of the ground) you will see the color of the 'surface of the ground.' ( green..when inverted).

 

You will also see ’9’ utility lines running under the ground and away from the houses ( away from each other). The “cubed” portion of the system represents 'under the ground' ...and begins at the base of the plane and goes ' downward' ( when inverted this will be represented by the light cream colored part of the system. )

 

The ground ( or surface) will now be green ( grass). The houses will be blue. The surrounding space around the houses will be as ...sunny as the sky. ( 3 dimensional area of space above the horizon of the 1 dimensional plane.= holograph!

 

Is this occurring all around us? Is this a way of realizing the ‘holographic scenario” as occurring relative to the “fabric of space-time?"

 

Does this proposal( postulate) “possibly” answer a “seeming” “impossible” …question…?

 

 

[md65536]

Label the circles 1, 2, 3, and the squares A, B, C

Draw them on a rectangle of paper.

 

 

Connect 1-A, 2-B, 3-C

then 1-B, 2-C, all with straight lines.

Connect 2-A with a curved line going around B, and then 3-A with a curved line going around C.

 

Connections 1-C and 3-B are missing.

 

Connect 1 to the middle of the left edge of the paper.

Connect C to the middle of the right edge of the paper (going up around 3).

Roll the paper into a cylinder, and 1-C will be connected.

 

Connect B to the middle of the top edge.

Connect 3 to the middle of the bottom edge (going around C).

Take the cylinder, and bend it into a donut. 3-B is now connected.

 

 

On a donut-shaped world, this would be possible with utility lines underground and not crossing. But that's not a plane.

 

In a donut-shaped universe, this would be possible with straight lines extending beyond the edges of the flat paper (and thus it's on a plane???).

 

 

It may seem unfeasible, but it's not really much harder than making an apple pie from scratch.

Edited September 2, 2011 by md65536

[probably wrong]

you guys with the pics just connected the 3 squares together then wen to 1 circle thats not what the rules state. its each square to each circle. and just for the heads up it isnt possible.

[TonyMcC]

This reminds me of another puzzle that is (also?) impossible to solve concerning the bridges of Konigsberg :- http://www.jimloy.com/puzz/konigs.htm

[John_gms]

I never expect BTs to be easy , this one is just like what I expected...

Check this one out -

http://www.iqtestexperts.com/brainteasers/

[SamSneed]

I'm not sure about who gave me this, but I've never seen it solved. Maybe you guys have, so here it goes:

 

Connect a line from each of the three squares to each of the three circles (nine lines in all) without crossing or going "under" or "above" a line. I believe the original brain teaser was phrased "Three houses need a gas line, water line, and electricity line, and all must be on the same plane underground."

 

You'd be best not to try and solve it; I did, and I can't find any solution. If there is one, you either know it or you don't. But go ahead and try if you think you can.

 

Can the circles and squares be rearranged? Meaning. Circle, square, circle on top and square, circle, square on bottom? Or some other variation.

Edited September 23, 2011 by SamSneed

[random]

I can complete it properly using mostly long curved lines as long as we are not committed to using the straight lines in the first drawing.

[imatfaal]

Random

 

Sorry but you havent - well not without moving off a single flat sheet of paper. Re-read the question - an perhaps you could have a look at the two proofs that it is impossible linked at the math forum

[genraven]

Maybe you can draw and connect the lines around the back of the paper

Edited October 20, 2011 by genraven

[chickenbutt]

untitled.bmpTHERE IS A SOLUTION YOU IDIOTS!!!!!!!!!!! a series of messing with peoples houses with lines, they are all on the same level but they dont cross all the rules are followed i will not respond to anything good day.

[matty]

Ohh, I remember the three houses needa gas line braintease!--I swore it had a resolution and thought you couldn't cheat with curved lines?--Anyway, I thought it was presented to us in toothpicks.

 

untitled.bmpTHERE IS A SOLUTION YOU IDIOTS!!!!!!!!!!! a series of messing with peoples houses with lines, they are all on the same level but they dont cross all the rules are followed i will not respond to anything good day.

 

Lol, well that is a crappy sketching.

[michel123456]

Does this break the rules?

 

[imatfaal]

The rules are normally given that the lines cannot cross nor pass through any of the houses. That is unless the puzzler wants to provide a solution in which can they remove the last proviso and your solution works