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."
Read it, if you haven't.
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...