📚 Chandigarh Police Constable – Reasoning Ability
Topic: Figure Series
Figure series tests your ability to spot patterns in a sequence of geometric shapes.
The challenge is to predict the next figure(s) in the series.
1. Simple Explanation
- Pattern Recognition: Each figure in the series is generated from the previous one by following a rule (addition, removal, rotation, scaling, color change, etc.).
- Rule Identification: Look at what changes (number of sides, orientation, size, color, position) and how it changes (increment, decrement, alternating, symmetrical, etc.).
- Extrapolation: Once the rule is identified, apply it to find the next figure(s).
2. Key Points to Remember
| Category | Typical Changes | Common Cues |
|---|---|---|
| Count | Number of shapes, vertices, or lines increases/decreases by a constant value | “+1”, “–2”, “×2” |
| Size | Shapes get larger or smaller uniformly | “scale factor”, “area ratio” |
| Orientation | Rotated 90°, 180°, etc. | “clockwise/anticlockwise” |
| Position | Shifted left/right/up/down, or moved in a pattern (zig‑zag, spiral) | “shift by one unit”, “diagonal” |
| Color | Alternating colors, new color introduced | “red → blue → red” |
| Shape Type | Triangle → Square → Pentagon, etc. | “new polygon appears” |
| Symmetry | Mirror image, rotational symmetry appears/disappears | “reflection about vertical axis” |
| Complexity | Number of sub‑figures within a figure changes | “two triangles → three triangles” |
Quick Checklist for Solving
- Count all elements in each figure.
- Note any size differences (side lengths, angles).
- Observe orientation changes (rotations, flips).
- Check position shifts (horizontal/vertical).
- Record color patterns.
- Look for structural changes (new shapes, added lines).
- Formulate a rule that explains all observations.
- Apply the rule to predict the next figure.
3. Worked Example
Series (illustrated with ASCII)
Figure 1: △
Figure 2: △△
Figure 3: △△△
Figure 4: △△△△
Step 1 – Observation
| Figure | Count of Triangles | Size | Orientation | Color |
|---|---|---|---|---|
| 1 | 1 | same | same | red |
| 2 | 2 | same | same | red |
| 3 | 3 | same | same | red |
| 4 | 4 | same | same | red |
Step 2 – Identify the Rule
- Number of triangles increases by 1 each step.
- No change in size, orientation, or color.
Step 3 – Predict Next Figure
- Next figure should have 5 triangles.
Answer:
Figure 5: △△△△△
4. More Challenging Example
Series
Figure 1: ▲
Figure 2: ▲◯
Figure 3: ▲◯△
Figure 4: ▲◯△◯
| Figure | Shapes in order | Observation |
|---|---|---|
| 1 | ▲ | Only triangle |
| 2 | ▲, ◯ | Added circle after triangle |
| 3 | ▲, ◯, △ | Added triangle after circle |
| 4 | ▲, ◯, △, ◯ | Added circle after triangle |
Rule: We alternate adding a circle and a triangle after the previous shape.
Next figure: Add a triangle after the last circle.
Figure 5: ▲◯△◯△
5. Quick Revision Summary
| What to Look For | Typical Rule | Quick Tip |
|---|---|---|
| Count | +1, –1, ×2, etc. | Write the counts; look for arithmetic/ geometric progression. |
| Size | Scale factor, similar triangles | Measure side ratios (if given). |
| Orientation | Rotate 90°, 180°, mirror | Check if each figure is a rotated version of the previous. |
| Position | Shift left/right/up/down | Track movement in a coordinate grid. |
| Color | Alternating colors, new color | List colors; look for alternation or pattern. |
| Shape type | New polygon appears | Notice new shape types appearing/disappearing. |
| Symmetry | Symmetry changes | Observe if figure becomes symmetrical or loses symmetry. |
| Complexity | Lines added/removed | Count lines or vertices; check for consistent increment. |
Final Advice
- Start with the obvious (count, color).
- Move to the subtle (orientation, position).
- Always test your rule on all given figures before predicting.
- Practice with varied patterns; the more you see, the quicker you spot the rule.
Good luck with your preparation! 🚓✨