Analogical Reasoning Examples: Finding Shared Structure Between Problems
A key and a password look nothing alike. Yet both can grant access. Analogical reasoning starts when the relationship matters more than the objects carrying it.
Analogical reasoning is the process of recognizing that two situations share a relational structure and using the better-understood case to interpret or solve the other one. The surface details may be very different. What survives is the pattern connecting the parts.
That is why analogies can appear in verbal questions, visual matrices, science explanations, troubleshooting, and everyday problem solving. The same basic move is happening each time: identify a relationship in one case, map the corresponding roles in another case, and check whether the relationship still holds.
Example 1: Key Is to Lock as Password Is to Account
Consider this simple analogy:
KEY : LOCK :: PASSWORD : ACCOUNT
The useful match is the relation grants access to. A key and a password share very few visible or physical features. A lock and an online account are equally different. The analogy works because the role structure lines up.
Research on analogy repeatedly finds that relational matches are central. In three studies, Gentner and Kurtz varied whether sentence pairs matched in their objects or in their relations. Relational matches were the main determinant of whether participants accepted a pair as analogous.
Example 2: Thermometer Is to Temperature as Speedometer Is to Speed
This example uses a more precise role relationship:
THERMOMETER : TEMPERATURE :: SPEEDOMETER : SPEED
The shared structure is instrument measures quantity. Once that relationship is identified, the individual objects become easier to map. Thermometer corresponds to speedometer because both occupy the “measuring instrument” role. Temperature corresponds to speed because both occupy the “measured quantity” role.
This is a useful reminder that analogy is not ordinary category matching. A thermometer is physically more similar to another handheld instrument than to a speedometer. Analogical reasoning asks which item plays the corresponding role.
Example 3: A Visual Transformation Can Be an Analogy
Visual reasoning questions often hide analogy inside shapes. Suppose figure A becomes figure B by rotating 90 degrees clockwise and adding one dot. Figure C contains a different shape. The missing figure D should apply the same transformation to C.
The objects have changed; the operation has stayed constant:
A → B maps to C → ?
Matrix questions often use this structure across rows and columns. One part of the grid demonstrates a relation; another part asks you to apply an equivalent relation elsewhere. The worked Matrix Reasoning Examples show several versions of that row-and-column logic, while the wider Pattern Recognition section connects this kind of transformation mapping with other rule-finding problems. Cognitive Train's Matrix Reasoning task then gives you a hands-on example of relational mapping.
When you try it, focus on the relationship between cells before comparing individual shapes. Ask what operation connects one state to the next, then look for the same operation in the corresponding part of the matrix.
Example 4: Surface Similarity Can Point You Toward the Wrong Analogy
Imagine two situations:
- A doctor must deliver treatment to a tumor while limiting damage to healthy tissue.
- An army must reach a fortress while avoiding dangerous concentrated force along one road.
The words, objects, and settings are very different. The shared solution structure can involve dividing a strong force into several weaker forces and converging them on the target.
This kind of cross-domain transfer became famous through experiments by Gick and Holyoak. Participants read stories that were superficially different from a later target problem. Transfer improved when comparison across multiple analogs helped participants abstract a more general problem schema. The quality of the induced schema strongly predicted later transfer performance.
The lesson is important: having a useful analogy in memory does not guarantee that you will notice it. Surface features can dominate retrieval. Comparing two examples can make the deeper structure easier to see.
Example 5: Similar Objects Can Hide Different Relations
Now reverse the problem. Two situations may contain similar-looking objects while expressing different relationships.
Suppose one picture shows a large circle containing a small triangle. Another shows a large circle beside a small triangle. The same objects appear in both. The relational structure differs.
Structural-alignment research captures this distinction. In four experiments, Markman and Gentner placed object similarity and relational similarity in competition. Their results supported the idea that comparison involves aligning structured representations and can draw attention toward matching relations.
For analogy questions, this means a tempting answer can share the right shapes, words, or categories and still be wrong if the roles do not align.
Example 6: Analogies Can Support New Inferences
The strongest analogies do more than tell you that two things are similar. They let you make a prediction.
Imagine that you understand how water pressure behaves in a pipe network. You then use the relationship as a rough model for current moving through an electrical circuit. Once corresponding parts are mapped, the familiar system can suggest what might happen in the less familiar one.
That inference still needs checking. An analogy transfers selected structure; it does not prove that every property carries over. Good analogical reasoning includes a final question: which relationships genuinely correspond, and where does the comparison stop?
Recent eye-tracking work also suggests that analogical mapping unfolds as an active comparison process. Kroczek, Ciechanowska, and Chuderski tracked participants solving analogy problems and studied how people established shared relational structure while mapping elements between cases.
Analogical Reasoning vs. Inductive Reasoning
The two abilities overlap, yet they answer different questions.
Analogical reasoning: “Does this relationship from one case map onto another case?”
Inductive reasoning: “What general rule can I infer from these observations or examples?”
Analogy can help induction because comparing cases may expose a shared rule. Induction can help analogy because a well-formed rule makes it easier to see which cases share structure. Cognitive Train's Inductive Reasoning Examples explores that neighboring process directly, and the Inductive Reasoning Test lets you practice rule discovery separately from analogical mapping.
A Quick Method for Solving Analogy Problems
- Name the relation in the source. Use a short phrase such as “measures,” “contains,” “causes,” “part of,” or “changes by rotation.”
- Assign roles. Decide what each element is doing inside that relation.
- Map the roles to the target. Ignore superficial resemblance when it conflicts with the relationship.
- Apply the relation. Predict the missing item, state, or outcome.
- Check the limits. Confirm that the mapped relation holds without assuming every property transfers.
This turns “these two things feel similar” into an explicit reasoning process.
Test the Broader Reasoning Skill
The embedded Matrix Reasoning task above gives you one visual form of analogical mapping. For a broader set of unfamiliar rule and relationship problems, continue with Cognitive Train's Abstract Reasoning Test.
You can also explore the wider brain tests collection or return to Cognitive Train's brain training and cognitive training tools.