Guide: How to Train Logic and Problem Solving

Introduction

In life, tasks where all conditions are neatly written down and a few answer choices are provided at the end are rare. More often, a person sees only part of the situation: equipment has stopped working, expenses do not match the plan, an opponent made an unexpected move, and explanations received from different people contradict one another. It is necessary to separate important facts from accidental details, put forward several assumptions, test them, and choose an action that brings you closer to the result.

This is precisely what we call problem solving. Logic is an important part of this process, but it does not exhaust it. It helps to move correctly from premises to conclusions, find contradictions, and understand what necessarily follows from known facts. However, real tasks often also require noticing a pattern, successfully representing the condition, abandoning an unsuccessful hypothesis, breaking the problem down into parts, or building a strategy several steps ahead.

A person with developed logic does not necessarily find every answer instantaneously. Their advantage often lies elsewhere: they understand better what they do not yet know, do not confuse assumption with fact, and can explain why a certain option is impossible. In a complex problem, this is often more important than a randomly guessed correct solution.

What is this skill

Problem solving begins with building an internal representation of the problem. A person needs to understand which objects are involved in the situation, what connections exist between them, what is allowed to be changed, and what result will be considered a solution. The very same condition may seem complex or simple depending on how it is presented. A table, diagram, drawing, or short list of constraints sometimes reveals a structure that is difficult to see in continuous text.

German psychologist Karl Duncker was among the first to systematically study the process of problem solving. He believed that a person does not simply cycle through random answers, but gradually changes their understanding of the problem. In the famous candle problem, participants were given a candle, matches, and a box of thumbtacks, and were asked to attach the candle to the wall so that wax would not drip onto the table. The solution emerged when the box began to be perceived not merely as a container for thumbtacks, but as a potential support. This experiment became a classic example of functional fixedness — the tendency to see an object only in its familiar role.

Hungarian-American mathematician George Pólya proposed one of the most famous problem-solving frameworks. It consists of four general stages: understand the problem, devise a plan, carry it out, and look back (check the result). This scheme seems obvious, but in practice, people often skip the first or last stage. They start calculating without clarifying the condition, or stop at the first answer obtained without checking whether it satisfies all constraints.

Logical reasoning can be deductive, inductive, or abductive. In deduction, the conclusion necessarily follows from the premises if they are correct. For example, if all shapes of a certain type have three sides, and a given shape belongs to this type, it also has three sides. Induction works differently: we observe several cases and formulate a general pattern. Such a conclusion may be well-grounded, but it is not guaranteed. Abduction is the search for the best explanation of the available facts. This is how detectives, doctors, engineers, and ordinary people often reason when trying to establish the cause of an unexpected event.

In puzzles about truth-tellers and liars, deduction from contradiction is particularly important. A person temporarily assumes that a certain statement is true and traces its consequences. If they contradict the condition, the initial assumption is rejected. This method is useful not only in puzzles. In a real situation, one can ask: "If my version were correct, what else should be observed?" The absence of an expected consequence sometimes exposes an error faster than searching for new confirmations.

The tendency to search specifically for confirmation of one's own version was studied by British psychologist Peter Wason. In one of his famous experiments, participants had to determine the rule behind a sequence of numbers. Many offered examples that fit their already conceived hypothesis, but hardly tested sequences capable of refuting it. Because of this, even a false rule could seem correct for a long time. This confirmation bias manifests in arguments, investigations, and strategic decisions: we are more willing to notice facts that support the first version.

Finding patterns is also not limited to simply continuing a numerical series. In progressive matrices, associated with the name of British psychologist John Raven, one needs to determine how shapes, the number of elements, directions, overlaps, or the arrangement of symbols change. The complexity lies in the fact that several transformations can occur simultaneously: one by rows, another by columns. A successful solution requires separating these changes and checking whether a single rule explains the entire matrix, rather than just an individual part of it.

Sometimes a problem has so many variations that a full search becomes impractical. Then heuristics are used — practical techniques that do not guarantee the shortest path, but help shorten the search. One can start with the most restricted element, eliminate clearly impossible options, work backward from the goal, or break the task into smaller subtasks. Psychologists Allen Newell and Herbert Simon described problem solving as a search in state space: there is an initial situation, possible operations, and a target state, and a person tries to find a sequence of transitions between them.

In strategic games, an opponent is added to this. It is not enough to find a move that improves one's position right now. One must consider the potential response of the other player, one's own next reaction, and the new configuration after several exchanges. That is why a good move can look modest: it does not yield an immediate benefit, but it restricts the opponent's answers or creates several threats at once.

What really helps to train it

Start with an accurate paraphrase of the condition. Before looking for an answer, state in your own words what is known, what needs to be found, and which constraints cannot be violated. If a problem contains many characters, numbers, or shapes, put them in a table or diagram. Often difficulties arise not because of logical complexity, but because part of the condition was lost in working memory.

Separate facts from assumptions. It is useful to explicitly mark: "this is stated in the condition," "this I deduced," and "this is merely my hypothesis." For example, if a character denies their guilt, the fact is only their statement, not their innocence. Such a division is especially important in tasks with lying, incomplete information, and several possible explanations.

Look for the strongest constraint. If one element can occupy only two spots, while others can occupy five or six, it is wiser to start with the first. In a numerical problem, this might be a rare sum; in a matrix, a cell affected simultaneously by row and column rules; in a strategic game, a threat to which there is only one safe answer. Working with the most constrained part reduces the number of options faster.

Do not try to see the complete solution immediately. Break the task down into intermediate questions. Which options are definitely impossible? Which element can be determined independently of others? What happens if you temporarily fix one variable? A small reliable conclusion often opens the way to the next one.

Use the method of assumption and verification, but do so systematically. Choose an option, trace its consequences, and mark where exactly a contradiction arose. You should not jump chaotically between assumptions, forgetting what has already been checked. In more complex tasks, it is useful to create a short decision tree: if A, then B and C are possible; if B leads to a contradiction, C remains.

Look for a way to refute your own version. After an attractive solution appears, ask what fact could prove it wrong. In a matrix, test the rule not only on the row where you noticed it, but on all the others as well. In a detective task, find out if the suspect explains every clue, not just the most striking one. In a game, test the opponent's strongest response, not the one you would find convenient.

Alternate between forward and backward search. Forward search starts from the available data: what can be deduced right now? Backward search starts from the goal: what would have to be true immediately prior to obtaining the desired result? In tasks involving the construction of a number, a route, or a sequence of moves, moving backward from the final state sometimes significantly reduces the number of options.

Learn to change the representation of the problem. If a verbal description confuses you, draw a diagram. If a drawing is overloaded, write the relationships using symbols. If numbers seem random, look at differences, sums, parity, number of repetitions, or positioning. Changing the form of representation does not change the problem itself, but it can make the hidden structure visible.

In matrices, analyze features separately. First check the number of elements, then shape, direction, color, fill, overlap, and position. Do not try to explain the whole drawing with one vague impression. A good rule should precisely show what happens in each row or column and allow you to predict the missing element.

In combinatorial tasks, avoid double-counting the same options. Establish an order of enumeration: for example, first by the first number, then by the second. Use symmetry to avoid analyzing equivalent situations multiple times. If swapping two identical elements changes nothing, it does not create a new solution.

In strategic games, consider short chains rather than a single move. For each candidate, ask: what is the opponent's strongest response, what will I do after it, and what will the position become? There is no need to calculate dozens of moves. Often two or three half-moves already weed out a solution that looked attractive only because of immediate gain.

After solving, do not limit yourself to checking the correct answer. Reconstruct the path: which fact was decisive, where did a false hypothesis arise, what allowed you to shorten the search? Then try to find another method. It is the analysis of the method that turns one solved puzzle into experience that can be useful in the next one.

It is useful to compare not only the number of correct answers, but also the nature of the errors. One person does not notice a pattern, another finds it but fails to check exceptions, a third understands the rule yet gets lost in the enumeration. They require different training emphases: searching for features, testing hypotheses, or organizing options.

Increase complexity gradually. At first, tasks may contain one clear rule, then two independent transformations, additional constraints, or the need to plan several steps ahead. If the difficulty increases too sharply, a person begins to guess and fails to form a reliable strategy.

It is also important to accept temporarily setting a task aside. Research on creative thinking has long connected breaks with the incubation effect: after a pause, people sometimes find a solution they did not see during continuous attempts. This is not magic brain activity in the background nor a guarantee of insight. A break can weaken an unproductive mindset and allow a return to the condition with a different representation.

The goal of logic training is not to memorize answers to hundreds of puzzles. It is more useful to form a set of mental habits: carefully read the condition, build an external representation, test consequences, search for contradictions, consider alternatives, and analyze your own path after completion. It is these operations that transform problem solving from a series of random guesses into a controlled process.

How to train logic and problem solving in BB Gym

Logic and problem solving in BB Gym are best assembled from several trainers, because each taxes its own side of the process. "Who's the Killer?" trains deduction from contradiction: you assume a statement is true, trace the consequences, and discard the version as soon as it contradicts the condition. "Raven's Matrices" teach separating features — quantity, shape, direction, overlap — and checking whether a single rule explains the whole matrix, not just an individual row; "Fluid Figures" provides the same work with hidden patterns. "Clock" provides good practice for backward search — moving backward from the desired result — while "Missing Numbers" habituates sorting through combinations systematically, without double-counting identical options. The games "Ternia", "NAONAO", "SIXTRI", and "LIMO" add an opponent and multi-step planning: for every move, it is worth asking what the opponent's strongest response is and what the position will be after two or three half-moves.

A Simple Routine and How to Read the Radar

It is more useful to train logic through mental habits rather than memorizing answers, so 3–4 short, deliberate sessions per week yield more than a guessing marathon. Before solving, paraphrase the condition in your own words and separate facts from assumptions; look for the strongest constraint with the fewest options, and do not grab the first attractive solution — try to find a fact that could refute it. The result lands on the "Logic" axis in the skill radar; the main score (0–1000) combines accuracy and speed, with accuracy unlocking speed — a quickly guessed answer without checking consequences is not progress. Compare yourself with yourself at the same difficulty level and look at the nature of your mistakes: whether you fail to see a pattern, see it but don't check exceptions, or get lost in enumeration — each case requires its own focus.

Finally

BB Gym helps transform problem solving from a series of random guesses into a controlled process, but it is an educational and entertainment tool, not a clinical test or diagnosis. A game score does not measure "intelligence level" in a medical sense, and an individual trainer does not "cure" anything. If difficulties with reasoning or planning noticeably interfere with studies, work, or daily life, it is worth consulting a qualified specialist rather than relying on game results.