Problem Solving Methods Applied to Chess

Chess strategy has the short-term aspect of choosing your next move and the longer-term aspect of planning, where the next move is just the 1st step of a longer-term strategy. In Main Ideas from Silman's How to Reassess Your Chess, I went over the main elements of a chess position for coming up with a plan.
https://lichess.org/@/DIAChessClubStudies/blog/main-ideas-from-silmans-how-to-reassess-your-chess/LpVTseL9

Chess analysis for a single move requires narrowing down the legal possible moves to a few candidate moves, and from those candidate moves, creating analysis trees to determine likely outcomes moving forward. In most positions, an analysis tree grows exponentially large beyond human capacity in just a few moves. Hence, players need to apply special problem-solving skills to navigate the near-infinite calculations, plans, counterplans, strategies, and more.
In a previous blog post, I analyzed Kotov’s Chess Candidate Moves & Analysis Trees.
https://lichess.org/@/DIAChessClubStudies/blog/kotovs-chess-candidate-moves-analysis-trees/RCBgdcrD

Chess is largely won in preparation, and basic problem-solving skills are of minimal use in an actual competitive game. Cognitive psychologists who have studied chess expertise explain that it takes thousands of hours of deliberate practice to master hundreds of thousands of patterns that allow experienced chess players to make complex calculations quickly.
https://lichess.org/@/DIAChessClubStudies/blog/chunking-theory-memory-techniques/FzEcLOrm
https://lichess.org/@/DIAChessClubStudies/blog/cognitive-dissonance-and-chess-improvement/H1i9q3so

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Basic Problem-Solving Strategies Applied to Chess.
People involved in chess education can use chess to teach these problem-solving strategies. Competitive chess players often study chess to win competitions or for the thrill of winning; however, chess can be studied outside of competition as a way to improve cognitive skills without trying to achieve a competitive victory. Chess can be applied to purify one's mind and improve problem-solving skills, affecting all mental activities. In areas where chess is taught in school, chess can be targeted as a way to increase test-taking skills and scores and create interest in math and science. In reality, chess is universal and can be targeted to improve mental activity for any skill.

I plan to write a series of blogs explaining how studying and teaching chess can be used to target specific skills. Here, I will briefly go over a few basic problem-solving skills, how they apply in chess, and how chess can increase one's ability in those problem-solving areas.

Method of Exhaustion - calculating every single option.
Trial & Error - randomly picking an option and testing to see if they work.
Divide & Conquer (Max / Min) - breaking problems into parts (start with biggest and move to smallest).
Process of Elimination - eliminate options that don't work.
Tit for Tat - respond in kind.

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Method of Exhaustion
The Method of Exhaustion, or Brute-Force Calculation, is the most important chess problem-solving strategy. I will devote a whole blog soon just on the Method of Exhaustion, its long history to ancient Greece, and its importance in computer algorithms. As most chess positions have multiple possible moves on each turn, the Method of Exhaustion is usually impossible. Even the greatest human minds can only calculate thousands of possibilities. However, a person using the Method of Exhaustion can induce a 'Flow State' and, over time, increase their calculation skills. Especially when teaching young children in school programs (with Steps Method, for example), students can rapidly increase their calculation skills.

As I often say, 'think and think until it hurts, then think some more!'

During play, the Method of Exhaustion is usually used only in forcing sequences such as tactics, exchanges, and endgames, where it is possible to calculate every possibility, and the consequences of such calculations are quite high. In practice sessions, students should spend regular periods of time practicing the Method of Exhaustion in more and more complicated positions as their calculation skills increase.

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Trial & Error / Process of Elimination
Trial & Error is generally a poor strategy for chess problem solving, but can still be useful in times of uncertainty or when solving chess puzzles. Trial and Error and Process of Elimination usually go together. For educators trying to increase test scores and interest in math and science, Trial and Error and Process of Elimination problem solving methods in chess can help general cognitive skills. Especially when using puzzles such as the Steps Method, where most puzzles can be solved with enough time by Trial & Error / Process of Elimination.

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Tit for Tat
Tit for Tat is a very important problem-solving skill in game theory, especially the Prisoner's Dilemma. I usually explain Tit for Tat with the example of the Golden Rule: 'You treat me with respect, I treat you with respect'. Mirroring other people's actions and responding in kind is a very important skill to master. Within chess, Tit for Tat is often most useful for coming up with a plan: if you can't decide what to do, mirror your opponent. As your opponent plays on the Kingside, you play on the kingside, or matching aggression with aggression. Tit for Tat is especially useful for chess as a method to teach morals and ethics, and the consequences of one's actions.

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Divide & Conquer (Max / Min)
Besides the Method of Exhaustion, which is used in forcing sequences or important parts of the game, Divide and Conquer is the most important problem-solving strategy in chess. As in most positions, the Method of Exhaustion is impossible; hence, one needs a strategy for calculating the most important aspects of the position. The most common Divide & Conquer (Max / Min) chess strategy is CCT (Checks, Captures and Threats). In critical positions, one should use the Method of Exhaustion: the Checks (which are forcing and require the opponent to respond), then Captures (if your opponent does not recapture, they will lose material), then Threats (usually threatening a check or a capture). For an advanced beginner or intermediate player in a slow time control game, they can use the Divide & Conquer (Max / Min) chess strategy of CCT (Checks, Captures, and Threats). As a student gains more tools in their toolkit, Divide & Conquer (Max / Min) will be the main method players use.

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I plan to elaborate in full detail on the Method of Exhaustion and the Divide & Conquer (Max / Min) problem-solving methods. Both of these have a long history and importance in math, logic nd computer programming. I will also explore how chess can be used by educators to specifically teach problem-solving skills in a way that increases test scores and general cognitive capacity.