*I found a detailed classification in an article by Murray Klamkin, cited below.*I added a few, and for some have not yet come across suitable examples. I would very much appreciate comments and additional examples. The most common way to approach a problem is by identifying a general class to which the problem belongs and using a method (if such exists) that is applicable to the problems of that class.

For a few more words and many additional examples see a separate file.

Very often, especially when a problem has been posed at an olympiad or in math circles, a solution that comes to mind first is not necessarily the best - the easiest to follows through.

Try one of the tactics, force yourself to speak aloud - something will come out.

Ray Bradbury, when short on ideas, taught himself to work with a dictionary picking random words and trying to put them together into something meaningful and relevant. Also, note that some of the tactics was previously mentioned - with additional advice - in a short assay of what constitutes a proof.

For the parallelipiped with sides $a,b,c$ and diagonal $d,$ we have $a^ b^ c^=d^.$ For a tetrahedron with three faces having right angles at the shared vertex and areas $A, B, C,$ $A^ B^ C^=D^,$ where $D$ is the area of the remaining face.

Being An argument by continuity assumes the presence of a continuous function whose properties could be used to solve a given problem.

Further reading I highly recommend the 1981 article The heuristic of George Polya and its relation to artificial intelligence by Alan Newell that offers penetrating analysis of Polya's problem solving heuristics prior to the discussion on its applicability to AI.

Specializaton, i.e., considering special cases, or introducing additional restrictions, while trying to solve a problem may highlight aspects of the original problem that have perhaps been missed at first glance.

It is incredibly powerful, although, at first sight, often appears innocuous.

The essence of WLOG is in making a random selection among a number of available ones for the reason of all possible variants being equipotent, i.e., leading to exactly same procedure and result.

## Comments Problem Solving Strategies Engel

## Math books - Art of Problem Solving

Problems in Algebra from the Training of the US IMO Team by Titu Andreescu. Problem Solving Strategies by Arthur Engel contains significant material on.…

## Problem-Solving Strategies - Arthur Engel Importado

Problem-Solving Strategies is a unique collection of competition problems over twenty major national and international mathematical competitions for high.…

## Problem-Solving Strategies

Jul 11, 2013. Engel, Arthur. Problem-solving strategies/Arthur Engel. p. cm. — Problem books in mathematics. Includes index. ISBN 0-387-98219-1.…

## Recommended Mathematics Literature

Problem-Solving Strategies. Arthur Engel. Springer, 1998. See this book at Amazon.com. A good initial preparation for IMO-style problem solving A Primer for.…

## Problem Solving Strategies - Project Maths

Problem Solving. Strategies. Trial and. Improvement. Draw a. Diagram. Look for a. Pattern. Act It Out. Draw a Table. Simplify the. Problem. Use an. Equation.…

## Strategy and Tactics in Problem Solving - Cut the Knot

One of the best problem solving strategies is do something; do not get and stay. Springer, 2007; A. Engel, Problem-Solving Strategies, Springer Verlag, 1998.…

## Good books on problem solving / math olympiad - MathOverflow

Polya's "How to Solve It" is a good one. When prepping for the Putnam, I used "Problem Solving Through Problems".…

## Arthur Engel mathematician - Wikipedia

Arthur Engel born 1928 is a German mathematics teacher, educationalist and prolific author. Engel's 1998 Problem-Solving Strategies has been described as the "most complete training book available for secondary and collegiate.…

## Problem-solving-strategiesBOOK 9- Problem Books in.

Angel Engel Institut f¨ur Didaktik der Mathematik Johann Wolfgang Goethe–Universit¨at Frankfurt am Main Senckenberganlage 9–11 60054 Frankfurt am Main.…

## Putnam at UCLA

The William Lowell Putnam Mathematical Competition Problems and Solutions 1938-1964, by A. M. Gleason. Problem-Solving Strategies, by Arthur Engel.…