An opaque fish bowl contains one fish, known to be either a piranha or a goldfish. A sushi lover drops a piranha into the bowl, shakes the bowl, and quickly withdraws one fish which proves to be a piranha. What is now the chance of removing a piranha? (Assume that during the time the two fish are in the bowl, one fish does not have time to consume the other fish.)
Stop. Think about this puzzle. Give it to friends to solve. The solution might surprise you.
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...
Another composer. He collaborated with Balanchine on the ballet Dreams.
Stop. Do you think any human in the world can identify this person simply by looking at these eyes?
Select the image to see answer.
The puzzles on this page were created by Cliff Pickover.