Figure Series – Reasoning Ability
(For Punjab Police Constable – Reasoning Ability Section)
1. Simple Explanation
A figure series is a sequence of geometric shapes (triangles, squares, circles, etc.) arranged in a particular order.
The task is to find the rule that governs the change from one figure to the next and then use that rule to predict the next figure or complete a missing one.
2. Key Points – What to Look For
| Attribute | Why It Matters | Typical Observations |
|---|---|---|
| Shape type (triangle, square, circle, etc.) | Shape may alternate or progress in complexity | Triangle → Square → Pentagon → … |
| Orientation (up, down, left, right, 45°) | Rotational patterns are common | ▲ → ► → ▼ → ◄ → ▲ |
| Size (length of sides, radius) | Scaling patterns (increase/decrease) | Side length 2 → 4 → 6 → … |
| Color or fill (solid, striped, dotted) | Color may alternate or repeat | Red, Blue, Red, Blue, … |
| Number of elements (dots, lines, sub‑shapes) | Counting patterns | 1 dot → 2 dots → 3 dots → … |
| Symmetry / Reflection | Mirror images or flips | Original → Mirror → Original |
| Position on the page | Shift left/right/up/down | Shift 1 unit right each time |
Tip: 3–5 figures are usually enough to deduce a rule. If two or more attributes change, try to isolate one that remains constant.
3. Common Figure‑Series Patterns
| Pattern | Example | How to Spot It |
|---|---|---|
| Rotational | ▲ → ► → ▼ → ◄ → ▲ | Each figure rotated by 90° clockwise |
| Alternating | Triangle, Square, Triangle, Square | Two shapes repeat alternately |
| Scaling (size) | Square side 2 → 4 → 6 → … | Size increases by a fixed amount |
| Adding Elements | 1 dot → 2 dots → 3 dots → … | Count of dots increases by 1 |
| Color Cycle | Red, Blue, Green, Red, Blue | Cycle through a set of colors |
| Reflected (mirror) | Original → Mirror → Original | Mirror image appears every second figure |
| Shape Complexity | Triangle → Quadrilateral → Pentagon → … | Each successive shape has one more side |
4. Step‑by‑Step Approach
-
List all given figures.
Write down shape, orientation, size, color, number of elements, position, etc. -
Identify constant attributes.
Which attribute stays the same? (e.g., all figures are solid fill) -
Find changing attributes.
Which attribute changes in a systematic way? (e.g., rotation by 90°) -
Formulate a rule.
Express the rule mathematically or descriptively (e.g., “rotate 90° clockwise each time”). -
Test the rule on the next figure.
Apply the rule to the last figure and verify that the predicted figure matches the pattern. -
Answer the question.
Choose the figure that satisfies the rule (or fill in the missing figure).
5. Worked Example
Series:
Figure 1: ▲ (triangle pointing up, solid, side 2)
Figure 2: ► (triangle pointing right, solid, side 2)
Figure 3: ▼ (triangle pointing down, solid, side 2)
Figure 4: ◄ (triangle pointing left, solid, side 2)
Figure 5: ▲ (triangle pointing up, solid, side 2)
Task: Identify the next figure (Figure 6).
Step‑by‑Step
| Step | Observation | Rule |
|---|---|---|
| 1 | All figures are solid triangles of the same size. | Constant shape & size. |
| 2 | Orientation changes: Up → Right → Down → Left → Up. | Rotation by 90° clockwise each step. |
| 3 | After the 5th figure (upward), the next rotation brings the triangle to the right side. | Next figure should be **► |