# Top 20 Ways to Solve a Problem

Published: 28 Nov 2007

**Divide and conquer**: break down large, complex problem into smaller, solvable problems**Hill-climbing strategy**, (or - rephrased - gradient descent/ascent, difference reduction) - attempting at every step to move closer to the goal situation. The problem with this approach is that many challenges require that you seem to move away from the goal state in order to clearly see the solution.**Means-end analysis**, more effective than hill-climbing, requires the setting of subgoals based on the process of getting from the initial state to the goal state when solving a problem.**Working backwards****Trial-and-error****Brainstorming**: a group creativity technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in the late 1930s by Alex Faickney Osborn, an advertising executive and one of the founders of BBDO, in a book called Applied Imagination. Osborn proposed that groups could double their creative output by using the method of brainstorming.**Morphological analysis**: a method developed by Fritz Zwicky (1967, 1969) for exploring all the possible solutions to a multi-dimensional, non-quantified problem complex.**Method of focal objects**: involves synthesizing the seemingly non-matching characteristics of different objects into something new.**Lateral thinking**: a term coined by Edward de Bono, a Maltese psychologist, physician and writer. It first appeared in the title of his book The Use of Lateral Thinking, published in 1967. De Bono defines lateral thinking as methods of thinking concerned with changing concepts and perception. Lateral thinking is about reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional step-by-step logic.**George PĆ³lya's techniques in How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)**: a small volume describing methods of problem solving. This book was published at Princeton University. It suggests the following steps when solving a mathematical problem**Research**: study what others have written about the problem (and related problems). Maybe there's already a solution?**Assumption reversal**(write down your assumptions about the problem, and then reverse them all)**Analogy**: has a similar problem (possibly in a different field) been solved before?**Hypothesis testing**: assuming a possible explanation to the problem and trying to prove the assumption.**Constraint examination**: are you assuming a constraint which doesn't really exist?**Incubation**: input the details of a problem into your mind, then stop focusing on it. The subconscious mind will continue to work on the problem, and the solution might just "pop up" while you are doing something else**Build (or write) one or more abstract models of the problem****Try to prove that the problem cannot be solved.**Where the proof breaks down can be your starting point for resolving it**Get help from friends or online problem solving community**(e.g. 3form)**Delegation**: delegating the problem to others.**Root Cause Analysis**: (RCA) is a class of problem solving methods aimed at identifying the root causes of problems or events. The practice of RCA is predicated on the belief that problems are best solved by attempting to correct or eliminate root causes, as opposed to merely addressing the immediately obvious symptoms. By directing corrective measures at root causes, it is hoped that the likelihood of problem recurrence will be minimized. However, it is recognized that complete prevention of recurrence by a single intervention is not always possible. Thus, RCA is often considered to be an iterative process, and is frequently viewed as a tool of continuous improvement.