Figure Series & Analogy – Logical Reasoning Study Notes
(For the NCO – Cyber Olympiad – Logical Reasoning Section)
1. What Are Figure Series & Analogy?
| Term | Simple Explanation |
|---|---|
| Figure Series | A sequence of shapes (dots, lines, polygons) that follows a visual pattern. You must spot the rule that connects all the figures and predict the next one. |
| Analogy | Two separate figure series are given. You need to find the relationship that links the first series to the second and then use that relationship to complete the second series. |
2. Why Is It Important?
- Cognitive Skill: Enhances pattern‑recognition, spatial reasoning and abstract thinking.
- Exam Utility: Widely used in competitive exams (IIT-JEE, NTA, SAT, etc.) and the Cyber Olympiad.
3. Types of Patterns in Figure Series
| Pattern | Example | Key Observation |
|---|---|---|
| Shape Transformation | Circle → Triangle → Square → Pentagon | Number of sides increases by 1 each step. |
| Size Variation | Small → Medium → Large → Medium → Small | Size fluctuates in a cycle. |
| Rotation / Direction | ▲ (0°) → ▲ (90°) → ▲ (180°) → ▲ (270°) | Same shape rotated 90° each step. |
| Color Coding | Red → Blue → Green → Red | Colors cycle through a set. |
| Number of Components | 1 dot → 2 dots → 3 dots → 2 dots → 1 dot | Number of dots follows a cycle. |
| Symmetry | Mirror left → Mirror right → Mirror left | Alternating mirror orientation. |
| Combination | Shape + Color + Size | Multiple attributes change together. |
4. Key Points to Remember
| # | Point | How to Apply |
|---|---|---|
| 1 | Identify Attributes – Shape, size, color, orientation, number of elements. | List each attribute for every figure. |
| 2 | Look for Cycles – Patterns often repeat every 2–4 figures. | Mark the cycle length. |
| 3 | Check Increment/Decrement – +1, –1, *×*2, /2, etc. | Compute differences between successive figures. |
| 4 | Use “All‑but‑One” Strategy – If 3 of 4 attributes change, the 4th is likely constant. | Keep the constant attribute unchanged. |
| 5 | Test Multiple Hypotheses – Don’t lock onto the first pattern; try alternatives. | Write down alternative rules and see which fits all figures. |
| 6 | For Analogies – Find the relationship (rule) that turns Series A into Series B. | Once the rule is known, apply it to the end of Series B. |
| 7 | Time Management – Spend 30–45 sec on each problem; move on if stuck. | Practice quick pattern spotting. |
5. Step‑by‑Step Strategy
- List All Figures – Write them in order.
- Break Down Attributes – Create a table:
Fig | Shape | Size | Color | Orientation | # of Elements - Spot Changes – For each column, note how the attribute changes.
- Determine Rule – Identify the simplest rule that explains all changes.
- Predict Next Figure – Apply the rule to the last figure.
- Validate – Check that the predicted figure satisfies all attributes.
6. Worked Example
Problem
Series: ▲ (Red, Small) → ◯ (Red, Medium) → ▲ (Red, Large) → ◯ (Red, Small) → ?
- ▲ = Triangle
- ◯ = Circle
Question: What is the next figure?
Solution
| Step | Action | Result |
|---|---|---|
| 1. List Figures | ▲, ◯, ▲, ◯, ? | |
| 2. Attributes | Shape: Triangle, Circle Size: Small → Medium → Large → Small Color: Red (constant) |
|
| 3. Identify Patterns | • Shape alternates (Triangle ↔ Circle). • Size follows a cycle: Small → Medium → Large → Small. |
|
| 4. Determine Rule | • Shape alternates every step. • Size cycles every 4 steps. |
|
| 5. Apply to Last Figure | Last figure (4th) is ◯ (Red, Small). Next shape = Triangle (alternation). Next size = Medium (cycle). |
|
| 6. Predicted Figure | ▲ (Red, Medium) |
Answer: Triangle, Red, Medium (▲ Red Medium).
Why This Works
- The rule is simple (alternating shape + 4‑step size cycle).
- All given figures satisfy it.
- The predicted figure is the only one that keeps both patterns intact.
7. Quick Revision Summary
- Identify all attributes