Conquer Club

I don't have a lot of patience for simple puzzles that probably have an obvious solution.... you try!



PUZZLE!

I see no one has solved it yet

every time I come so close! It's a good puzzle and I think there is a solution

There is one if you go three-dimensional, otherwise it's impossible.

You can only solve it if you "roll it up" so it forms a tube.

not sure if it is possible

reptile wrote:not sure if it is possible

It isn't - MeDeFe expained.

Guilty_Biscuit wrote:

reptile wrote:not sure if it is possible

It isn't - MeDeFe expained.

yeah it's impossible.

was . so . close

piece of pish. Easy.

heavycola wrote:piece of pish. Easy.

care to post a solution?

I'm prepared to take Heavycola at his word. I haven't actually attempted it, but it looks simple enough to me.

haha you wish!

In fact, it looks so simple, it's not worth my while attempting it.

Balsiefen wrote:

heavycola wrote:piece of pish. Easy.

care to post a solution?

My bad. Sorry Dave.

jay_a2j wrote:I don't have a lot of patience for simple puzzles that probably have an obvious solution.... you try!



PUZZLE!

this is a good way to trick people, i'm sorry to say i've seen this puzzle before and it literally has no solution!

jay_a2j wrote:I don't have a lot of patience for simple puzzles that probably have an obvious solution.... you try!



PUZZLE!

dammit its blocked

i'll try it either when i go to clark or go home

Mathematically impossible in two dimensions.

a 3D cylinder will do the trick

Impossible..on the best you're one line short, but it won't have any way to get to the last house with crossing a line.

I solved it!

I so wanted to be the one who said that but I was trying for 30 mins and still no luck

Daring Overlord5 wrote:a 3D cylinder will do the trick

Actually, a cylinder will not do the trick (assuming you mean the surface of a cylinder). A cylinder is topologically identical to a plane with a hole. Removing a point from a plane will not allow this problem to be solved. No solution to this puzzle exists in any 2-d geometry.

Here is a simple proof that no 2-d solution exists.

Let A1, A2, A3 be houses; B1, B2, B3 be utilities.
Connect B1 with A1 and A2.
Connect B2 with A1 and A2, without crossing previous lines.
Thus, A1 - B1 - A2 - B2 - A1 represent a closed path encircling some region of space; call this region R1.

Case 1 - One of A3/B3 is inside R1, the other is outside R1.
Thus, since R1 represents an enclosed region, there is no path which connects A3 and B3 without crossing the boundary.

Case 2 - Either both A3 and B3 are inside R1, or both are outside. WLOG, assume both are inside.
Connect B1 and B2 to A3. Thus, R1 has been bifurcated into two new regions, R2 = A1 - B1 - A3 - B2 - A1; and R3 = A2 - B1 - A3 - B2 - A2.
Then B3 must be inside either R2 or R3; WLOG assume B3 is inside R2.
Note that A2 is outside R2. Thus, there is no path which connects B3 and A2 without crossing a boundary.

Therefore, in all cases, there will be at least one connection which cannot be made.

QED.

This proof works for any 2-d geometry. It's not quite as rigorous as it could be; if I had the inclination and the time, I could build a similar proof working from the definitions of open and closed sets in a 2-d metric space, but frankly I don't care. This is a problem than any high-school geometry student ought to be able to solve by construction; it disappoints me that the answer is not readily apparent to all here.

Actually... upon reconsideration, a torus geometry will allow you to solve the problem. A torus is slightly higher dimension than a plane, though, so I think I standby my statement at the problem in insoluble for all geometries >= 2-d.

impossible is nothing

er..i tried and i couldnt do it..it seemed so simple i didn't believe you guys couldn't solve it..then i actually tried to do it