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You are probably most familiar with lateral thinking problems which are puzzles or riddles. They lead you to make certain assumptions, and to solve them you have to look at those assumptions you're making and try to get beyond them. Here is a short example of this type:
The book store owner used one book to destroy thousands of others - all in one day. How did he do this? A lateral thinking puzzle like this relies on setting your thoughts in a certain direction. In this case, the idea of a "book store owner" encourages you assume that a book one reads was used to destroy the others. Drop that assumption and you might find the solution - the man used a book of matches to burn all the other books.
Puzzles of this type are good mental exercise, and fun, but fortunately not all lateral thinking problems are word play or simple riddles. In fact, many are designed to require or encourage creative thinking in ways more applicable to actual situations. This type often has many solutions which are valid.
Some may not like the inconclusive nature of this kind of puzzle or problem. They want one definitive solution, so they know they're "right" once they have an answer. However, these more open-ended lateral thinking problems are just as good for exercising one's creativity, and the thinking skills developed from working on them may be more applicable to everyday life, where there is rarely one definitive solution to a problem.
This type usually involves a scenario or situation which is explained, along with a goal. Suppose, for example, you need to get a basketball out of a 12-foot deep pit. That's the goal. The situation? The pit has smooth cement for the floor and walls, and it is square, about four feet per side. You're alone and have only what you are wearing, including whatever is in your pockets at the moment. How can you get the basketball out using only what has been described?
Like any good lateral thinking problem this requires you to think "laterally," which means coming at the problem from other angles, as opposed to the more traditional linear or logical way. You have to use what you have, but in ways that these things are not normally used.
You might, for example, make a "basket" out of your t-shirt, tying your shoelaces to it around the edges. Unravel the threads from your socks and you can make a string to lower the "basket." Then move the basketball onto it and then pull it up to you. A shoe hung on the end of a string made of strips of clothing might work to "kick" the ball into place, rolling it onto your shirt.
Of course, life itself presents us with many lateral thinking problems, if we approach situations creatively. A judge in a Michigan child custody case could have followed the traditional thinking about how much time the children would spend at each parent's place, but he ruled that the children would stay right where they were in the home they knew. The parents would each get their own place and move in with the kids on alternating weeks. Now that's a good example of applying lateral thinking to real life problems.
Note: See the page Lateral Thinking Examples for a look at some creative solutions to a real scenario.