Missing Numbers

Missing Numbers questions involve identifying the number that logically completes a given sequence or pattern in a grid, matrix, triangle, or numerical series.

These questions test your:

• Logical reasoning

• Number sense

• Pattern recognition

• Arithmetic and analytical ability

🧩 Types of Missing Number Questions

1. Matrix/Grid-Based Puzzles

• 3x3 or 4x4 grids with a pattern across rows/columns/diagonals

• You find a logic that fits row-wise or column-wise

2. Arithmetic Sequences

• Series like 2, 4, 6, ?, 10 (even number pattern)

3. Geometric Sequences

• Numbers multiplied or divided by a constant factor

4. Mixed Operations

• A mix of +, −, ×, ÷ with increasing/decreasing logic

5. Magic Squares or Crosses

• Total of rows/columns equals the same number

6. Clockwise/Anti-clockwise Patterns

• In a circle or triangle, pattern follows a direction

🔢 Common Patterns and Formulas

Pattern Type	Explanation	Example
Addition	Adding fixed or increasing numbers	2, 4, 6, 8, ? → 10
Multiplication	Constant multiplication or product logic	2, 4, 8, ? → 16
Squares/Cubes	Use of perfect squares or cubes	1, 4, 9, ?, 25 → 16
Difference	Subtracting constant/increasing numbers	20, 18, 15, ?, 8 → 11
Alternating	Two different series alternating between terms	2, 5, 4, 7, 6, ? → 9
Diagonal/Matrix	Use row/column/diagonal rules	Explained below

🔍 Examples and Explanations

🔸 Example 1: Row-Based Matrix Logic

| 2 | 3 | 5 |
| 4 | 5 | 9 |
| 6 | ? | 15 |

👉 Solution:

• Row-wise pattern:
  Row 1 → 2 + 3 = 5
  Row 2 → 4 + 5 = 9
  Row 3 → 6 + ? = 15
  → ? = 9

🔸 Example 2: Column-Based Logic

| 3 | 6 | 9 |
| 2 | 4 | 6 |
| 1 | 2 | ? |

👉 Check column-wise subtraction:

• Col 1: 3 - 2 = 1

• Col 2: 6 - 4 = 2

• Col 3: 9 - 6 = 3
  ✅ Answer: 3

🔸 Example 3: Triangle with Numbers

   [3]
 [2] [1]

Logic: 2 + 1 = 3
Another:

   [?]
 [4] [5]

4 + 5 = 9

✅ Missing number: 9

🔸 Example 4: Circle Pattern

  [5]
[2]   [3]

2 + 3 = 5 → Center
Similarly:

  [?]
[4]   [6]

4 + 6 = 10

✅ Missing number: 10

🔗 Strategies to Solve

1. Check row-wise and column-wise logic

2. Look for simple operations first: +, −, ×, ÷

3. Try difference of squares, multiplication chains

4. Check diagonals or symmetrical logic

5. Attempt reverse logic if needed

💡 Tips and Tricks

• Try all directions (row, column, diagonal)

• Look for unit digit patterns

• Use options to back-calculate

• Use logic elimination for faster solving

• Skip and come back if stuck—don’t waste time on one

📝 Practice Question Set

Question Type	Question	Answer	Explanation
Matrix Logic	1 2 3 / 4 5 9 / 7 ? 17	10	7 + ? = 17
Arithmetic	5, 10, ?, 20	15	+5 sequence
Alternate	2, 6, 4, 8, 6, ?	10	+2 alternates
Triangle	Top: ?, Base: 5 & 4	9	5+4=9
Clockwise	Top: ?, Left: 3, Right: 5	8	3+5=8

📚 Summary

• Missing Numbers test your ability to identify number patterns

• Appear in matrix, sequences, triangle or diagram-based

• Start with basic operations and build up

• Master common patterns and formulas

• Practice different types to boost speed