*If you're looking for lateral thinking puzzles, see Lateral Thinking Puzzles*.

The term "**lateral thinking**" was coined by Edward De Bono in his 1971 book Lateral Thinking, although the concept itself dates back much earlier. Lateral thinking refers to a problem solving technique that emphasises looking at problems in **novel and creative ways**, by employing methods that may be **unorthodox** or **not strictly logical**, as opposed to tackling a problem directly using traditional logic. Some of the main principles of lateral thinking are:

*generating a large number of potential alternative solutions**challenging assumptions**suspending judgement*on alternatives.

Lateral thinking can be contrasted with what might be called "vertical thinking," thinking that is concerned with taking a single idea and pursuing it to its conclusion. Lateral thinking, on the other hand, is concerned with generating as many ideas as possible, not with evaluating and pursuing those ideas. Effective problem solving requires both vertical and lateral thinking.

How can you use lateral thinking in mathematics? Just as lateral thinking can be useful in solving problems in other disciplines, it is useful in solving mathematics problems. For example, examine the page about heuristics for solving math problems; many of these heuristics involve examining various alternatives or possibilities; being able to generate many alternatives can help you to find the ones that will lead to a solution.

For an example of how lateral thinking can be used, consider these two word problems. First:

A typist can type 15 pages in an hour. How many pages can five typists type in an hour?

Answering the question mathematically, we would multiply: 15 pages/hour × 5 = 75 pages/hour. In the real world, assuming the speed of the typist to be typical, this is probably close to the correct answer.

Now consider the following problem:

A construction worker can dig a hole two feet deep in ½ hour. How deep a hole can five construction workers dig in ½ hour?

The form of this question is rather similar to the first one, so we might be tempted to tackle it in the same manner. Mathematically, the answer would be 2 feet × 5 = 10 feet. However, in the real world, the answer would most likely be much less than 10 feet. To find the correct answer, we will need to consider the following possibilities:

- As a hole becomes deeper, it needs to also become longer and wider or else the dirt at the sides of the hole might give way or the hole will become increasingly difficult to excavate. So, the increase in the amount of dirt removed is more likely to be closer to 5³ = 125 than to 5, so the increase in depth is more likely to be closer to ∛5 than it would be to 5.
- If five workers are crowded into a small area, they will get in each other's way, making each of them less productive. The extra dirt removed from the hole will add to the congestion unless time is diverted from digging to hauling it away.
- In order to work together, the workers will need to communicate with each other; the more time spent doing that, the less time available for digging.
- As one digs deeper, the soil is often harder and more difficult to remove.

So, we should not be surprised if the real world answer is only slightly greater than 2! Whatever the actual answer is, it violates our mathematical intuition. That doesn't mean that either the answer or our mathematical intuition is wrong; it's just that mathematical concepts don't always map precisely to the real world.

One fun application of lateral thinking is in lateral thinking puzzles. Just like lateral thinking itself, lateral thinking puzzles pre-date the invention of the term "lateral thinking;" you may see the term "intellograms" in works from the first half of the twentieth century, and they are also referred to as "situation puzzles" or by other names. Lateral thinking puzzles are often embellished with a story. In such a puzzle, a story, often containing inexplicable, improbable, or unusual details, is presented, and the task of the solver is to find a rational explanation for the story.

You can solve lateral thinking puzzles on your own, but they are often played in a group, with one person, who knows the answer, hosting the puzzle, and the other people asking the host yes/no questions until someone is able to explain the scenario.

The following is a well-known example of a lateral thinking puzzle:

Eric walks into a bar, and asks the bartender for a glass of water. The bartender hesitates, and then pulls out a gun and points it at Eric. Eric is startled momentarily, but after a minute or so thanks the bartender and leaves. Why?

The answer? Eric had hiccups. The bartender, realizing why Eric was asking for water, decided to try to scare the hiccups out of Eric, which was successful.

If you are interested in lateral thinking puzzles, there are five pages of lateral thinking puzzles on Math Lair. Go to page 1, page 2, page 3, page 4, page 5.

Lateral thinking puzzles can also be a good way of warming up the brain to tackle other topics requiring creative thinking, such as mathematics. Mathematics teachers often use lateral thinking puzzles for this purpose.

Related articles: Lateral thinking can be considered to be the complement of critical thinking.

Sources used (see the bibliography page for titles corresponding to numbers): 33.

External links: Bibliography of classic lateral thinking puzzles.