Coding-Decoding | Delhi Police Exam

1. What are Missing Numbers?

Missing Numbers involve finding the missing element in a sequence or pattern based on mathematical operations, logical rules, or specific arrangements. These questions test your pattern recognition and analytical skills.

Pattern Recognition

Mathematical Operations

Logical Sequences

Analytical Thinking

Simple Definition: Missing Numbers are pattern-based problems where you need to identify the logical rule and find the missing element in a sequence, table, or arrangement.

Types of Missing Number Problems

Common Problem Types

Type	Description	Example
Number Series	Missing number in sequence	2, 4, 6, ?, 10
Matrix Problems	Missing number in grid/table	3×3 grid with one missing
Mathematical Operations	Based on arithmetic operations	5 + 3 = 8, 7 + ? = 15
Clock & Calendar	Time and date patterns	Missing time/date in sequence
Alphanumeric Series	Combination of letters & numbers	A1, B2, C3, D?
Figure Series	Patterns in geometrical figures	Missing number in shapes

2. Common Patterns in Missing Numbers

Frequently Used Patterns

Arithmetic Patterns

Constant Difference

2, 5, 8, 11, 14 (+3)

Increasing Difference

2, 4, 7, 11, 16 (+2,+3,+4,+5)

Alternating Pattern

2, 4, 3, 6, 5, 10

Geometric & Special Patterns

Multiplication Pattern

3, 6, 12, 24, 48 (×2)

Square/Cube Series

1, 4, 9, 16, 25 (1²,2²,3²...)

Prime Numbers

2, 3, 5, 7, 11, 13

3. How to Solve Missing Number Problems?

Follow these step-by-step methods to solve missing number questions:

1

Observe the Sequence

Look at all given numbers carefully

2

Check Differences

Find differences between consecutive terms

3

Identify Pattern Type

Arithmetic, geometric, square, etc.

4

Apply Pattern & Verify

Find missing number and check with other terms

4. Matrix Missing Number Problems

Common Matrix Patterns

Pattern Type	Description	Example
Row-wise Pattern	Same operation in each row	2,4,6 → +2 pattern
Column-wise Pattern	Same operation in each column	3,6,9 → ×2 pattern
Diagonal Pattern	Pattern along diagonals	Top-left to bottom-right
Sum/Product Pattern	Rows/columns have equal sums	Magic square patterns
Combination Pattern	Multiple operations combined	Addition & multiplication together

5. Solved Examples

Example 1: Number Series

Find the missing number: 5, 11, 23, 47, ?

Step 1: Check differences: 11-5=6, 23-11=12, 47-23=24

Step 2: Differences are doubling: 6, 12, 24

Step 3: Next difference = 24×2 = 48

Step 4: Missing number = 47 + 48 = 95

Answer: 95

Example 2: Matrix Problem

Find missing number in the matrix:

2	4	6
3	6	9
4	8	?

Step 1: Row 1: 2,4,6 → ×2, ×1.5

Step 2: Row 2: 3,6,9 → ×2, ×1.5

Step 3: Row 3: 4,8,? → ×2, then ×1.5

Step 4: Missing number = 8 × 1.5 = 12

Answer: 12

Example 3: Mathematical Operation

If 3☆5=16, 4☆7=30, 5☆9=48, then 6☆11=?

Step 1: Analyze pattern: 3☆5=16 → 3×5 + 1 = 16

Step 2: Check: 4☆7=30 → 4×7 + 2 = 30

Step 3: Check: 5☆9=48 → 5×9 + 3 = 48

Step 4: Pattern: a☆b = a×b + (a-2)

Step 5: 6☆11 = 6×11 + (6-2) = 66 + 4 = 70

Answer: 70

6. Special Number Patterns

Important Number Sequences

Mathematical Sequences

Fibonacci Series

1, 1, 2, 3, 5, 8, 13, 21...

Triangular Numbers

1, 3, 6, 10, 15, 21...

Square Numbers

1, 4, 9, 16, 25, 36...

Special Series

Prime Numbers

2, 3, 5, 7, 11, 13, 17...

Cube Numbers

1, 8, 27, 64, 125...

Alternating Series

1, 4, 3, 6, 5, 8, 7...

7. Quick Recap

Pattern Type	Key Feature	Example
Arithmetic	Constant difference	5, 8, 11, 14 (+3)
Geometric	Constant ratio	2, 6, 18, 54 (×3)
Square Series	Squares of numbers	1, 4, 9, 16, 25
Prime Numbers	Divisible by 1 and itself	2, 3, 5, 7, 11
Fibonacci	Sum of previous two	1, 1, 2, 3, 5, 8

8. Delhi Police Exam Tips

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Check differences first - most common pattern

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Look for multiple operations - addition, multiplication, etc.

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Memorize special sequences - primes, squares, Fibonacci

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Verify your answer - check if pattern works for all terms

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Practice matrix problems - row, column, diagonal patterns

Missing Numbers