## Twisted Wires

A forum for good logic/math puzzles.

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Transhooman
Posts: 4
Joined: Wed Jul 14, 2010 8:34 pm UTC

### Twisted Wires

Here is a nifty little puzzle I found 9 or so years ago.
It still like showing it to people. It's one of my favourites.

It's called "Twisted Wires", and was created by Clifford Pickover.
He is the guy who wrote "Sex, Drugs, Einstein and Elves."

The Puzzle:

The description from his website:
Is it possible to connect the boxes without crossing lines? Interestingly, many scientists surveyed could not solve this problem.

The task of interconnecting electrical components in circuits is an important one, and a problem which computers are increasingly being used to solve. I have studied the following wiring problem, not with a computer, but rather with 450 scientists in order to test their ability to solve a seemingly simple looking geometric problem. The problem is stated as follows. Given the six boxes (represented by enclosed regions A, B, C) in the figure, is it possible to connect box A to A, B to B, and C to C with lines which do not cross or go outside the surrounding frame? Your lines may be curvy, but they cannot touch or cross each other, or touch any other line in the drawing. In my study, I asked people to time themselves as they attempted to arrive at a solution. About twenty percent of the scientists surveyed said this problem was impossible to solve.

The problem is in fact solvable, and the solution is left as an exercise for you. If you cannot solve the problem, don't think about it for a day, and then return to the problem. Many of the people I tested found it easier to solve this on their second attempt a day later. A computer could probably solve this class of problems faster than a human; however, humans have one advantage in that they have the ability to discard bad attempts rather quickly.

Can you write a computer program to randomly place squares within the figure in order to create new and unusual wiring problems?

Psychologists have long been interested in the relationship between visualization and the mechanisms of human reasoning. What is the significance of the fact that people find the puzzle easier to solve after returning to it a day later? Is there any correlation in a person's ability to solve the puzzle with sex, profession, artistic ability, etc.? Let me know...

jestingrabbit
Factoids are just Datas that haven't grown up yet
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Location: Sydney

### Re: Twisted Wires

Spoiler:
Not that tricky.

connec.gif (14.42 KiB) Viewed 3705 times

Initially I stared at it and thought it impossible. But then it just clicked.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

jaap
Posts: 2094
Joined: Fri Jul 06, 2007 7:06 am UTC
Contact:

### Re: Twisted Wires

jestingrabbit wrote:Initially I stared at it and thought it impossible. But then it just clicked.

Yes, it is easy once you have the following insight:
Spoiler:
The B-B link divides the space into two unconnected regions.
The left region contains the bottom left A, so must also contain the other A.
The right region contains the bottom right C, so must also contain the other C.
Therefore the B-B link must go around the left of the top C and the right of the top A.
You can do this in either order to create two distinct solutions.

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: Twisted Wires

Spoiler:
jaap wrote:You can do this in either order to create two distinct solutions.

Yeah, there's a symmetry there. Though the large gap suggests the solution I gave imo.

I actually came at it from a different process than the one you describe. I thought that maybe it was a bit of a 169, with a connection joining the Bs via the boundary. Having mentally done that, I wondered how to solve the sub problem of connecting the As and Cs. But having done that sub problem, the larger problem just clicked.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

rigwarl
Posts: 759
Joined: Wed Dec 09, 2009 9:36 pm UTC

### Re: Twisted Wires

Spoiler:
It's interesting that trick behind the puzzle relies completely on how the letters are ordered; specifically, that you don't do B last.

I realized this because I just happened to connect the C's and the A's as the first two. At that point, it doesn't matter how you connected them- there will ALWAYS be a solution for B if you connect it last (additionally, making the first two connections are trivial).

Jammerjoint
Posts: 15
Joined: Thu Jul 15, 2010 2:34 am UTC

### Re: Twisted Wires

Spoiler:
Took like...30 seconds? Is it really that challenging? My thought process:

1. B to B appears to be the main obstruction
2. A to A and C to C are symmetrical/interchangeable
3. Single loop around floating block does not work
4. Double loop does - done

imatrendytotebag
Posts: 152
Joined: Thu Nov 29, 2007 1:16 am UTC

### Re: Twisted Wires

Spoiler:
Oddly enough, the biggest hint for me was that the puzzle was, in fact, solvable. I spent the first minute trying to prove it was impossible, then looked at the quoted text, then came up with an answer pretty quickly.
Hey baby, I'm proving love at nth sight by induction and you're my base case.

mr-mitch
Posts: 477
Joined: Sun Jul 05, 2009 6:56 pm UTC

### Re: Twisted Wires

Spoiler:
sol.jpg (21.93 KiB) Viewed 3428 times

Dhes
Posts: 125
Joined: Thu Nov 22, 2007 11:27 am UTC
Location: Netherlands
Contact:

### Re: Twisted Wires

Spoiler:
Didn’t time my self, but I think it was about 10 seconds, I solved it before I started reading the quote.
If you do a lot of PCB (circuit boards) designing it’s not much of a challenge.
Just for fun I put it in UltiBoard (PCD design program), it did it in les than a second.
I’m dyslexic, so I tent tot pull things way out of contacts.