Figure series: Reasoning Ability Notes for Maharashtra PSC

Figure Series – Reasoning Ability (Maharashtra PSC)

Figure Series is a popular type of question in reasoning sections where you are given a set of geometric figures arranged in a row/column or matrix and you must predict the next figure or fill in the missing one.
The key is to identify the rule that governs the change from one figure to the next.

1. Simple Explanation

Step	What to Look For	Why It Matters
1. Identify the elements	Shape type (square, circle, triangle, etc.), size, color, orientation, number of sides, symmetry, etc.	Every feature can change; all are potential clues.
*2. Check the position* rule**	Horizontal/vertical translation, shift, rotation or reflection.	Many series are based on moving the figure along a line.
3. Look for incremental changes	Number of sides increases by 1, radius increases, color changes, etc.	Numerical patterns are straightforward to spot.
4. Examine repetitions or cycles	After 3 or 4 figures the pattern repeats.	Helps to anticipate the next figure.
5. Combine multiple rules	Sometimes shape changes and position changes simultaneously.	Complex series often require two or more rules.

Tip: Always start with the simplest rule (translation, rotation). If it fails, move to more complex ones.

2. Key Points

Category	Common Rules	Example
Transformation Rules	• Translation – shift right/left/up/down • Rotation – 90°, 180°, 270° clockwise or counter‑clockwise • Reflection – flip horizontally or vertically	1️⃣ ➜ 2️⃣ (shift right 1 unit) ⬜ ➜ ⬛ (rotate 90°)
Morphology Rules	• Addition/Subtraction of sides (triangle → square → pentagon) • Size change (radius increases by 1 cm) • Color change (red → green → blue)	🔺 ➜ 🔻 ➜ 🔺 (alternating shape)
Symmetry Rules	• Mirror symmetry – left side mirrors right side • Radial symmetry – identical sectors around a center	4‑sector pattern where each sector rotates 90°
Pattern & Repetition	• Cycle length (every 4th figure repeats) • Alternating pattern (odd/even positions differ)	1️⃣, 2️⃣, 3️⃣, 1️⃣, 2️⃣, 3️⃣ …
Combination Rules	• Shape changes while moving along a line • Size increases and orientation changes simultaneously	🔺 (left, small) ➜ ⬛ (right, larger) ➜ 🔺 (right, bigger)

How to Approach a Question

Write down the figure in a simple form (symbols, side counts, colors).
Check horizontal/vertical progression: Are the figures moving?
Check shape progression: Are the shapes changing?
Look for numeric patterns: Side count, radius, number of dots, etc.
Test a hypothesis on a few figures; if it fits all, use it for the next figure.
If multiple rules fit, the simplest one is usually the intended answer.

3. Worked Example

Question

Figure 1:  ▲  (triangle)
Figure 2:  ■  (square)
Figure 3:  ▲  (triangle)
Figure 4:  □  (square)
Figure 5:  ▲  (triangle)
Figure 6:  □  (square)
Figure 7:  ?

Solution Steps

Identify the pattern in shape
- Triangles and squares alternate every figure.
- Sequence: ▲, ■, ▲, ■, ▲, ■, ...
Check for other changes
- No change in size, color, orientation.
- Pattern is purely alternation.
Predict the next figure
- Since Figure 6 is a square, the next must be a triangle.

Answer: ▲ (triangle)

Another Example with Transformation

Figure 1:  ⬛ (square)
Figure 2:  ⬛ (square) rotated 90°
Figure 3:  ⬛ (square) rotated 180°
Figure 4:  ⬛ (square) rotated 270°
Figure 5:  ⬛ (square) rotated 360° (back to original)
Figure 6:  ?

The rule: rotate the square 90° clockwise each time.
After 5 rotations, the square is back to its original orientation.
The 6th figure will again be rotated 90°.

Answer: ⬛ rotated 90° clockwise (same as Figure 2)

4. Quick Revision Summary

Always start with the simplest rule: translation → rotation → reflection.
Look for side count changes: 3→4→5 sides, radius increments, etc.
Check for alternation: odd/even positions may