Logical Reasoning • Topic 1 of 3

Mathematical Puzzles and Logical Sequences

What are Mathematical Puzzles?

Mathematical puzzles are problems that require logical thinking, pattern recognition, and mathematical skills to solve. They are like brain teasers that make you think creatively.

What are Logical Sequences?

Logical sequences are ordered arrangements of numbers, letters, or shapes that follow a specific rule or pattern. Identifying the rule helps you predict the next element in the sequence.

Common Types of Number Sequences:

Type	Description	Example	Rule
Arithmetic	Constant difference	3, 7, 11, 15, ...	Add 4
Geometric	Constant ratio	2, 6, 18, 54, ...	Multiply by 3
Square numbers	Perfect squares	1, 4, 9, 16, 25, ...	n²
Cube numbers	Perfect cubes	1, 8, 27, 64, 125, ...	n³
Fibonacci	Sum of two previous	1, 1, 2, 3, 5, 8, 13, ...	Add previous two
Prime numbers	Prime numbers	2, 3, 5, 7, 11, 13, ...	Next prime

Tips for Solving Puzzles and Sequences:

Look at the differences between consecutive terms
Check for multiplication or division patterns
Look for alternating patterns (two interleaved sequences)
Check for position-based patterns (nth term formula)
Consider digital patterns (sum of digits, etc.)
Look for visual patterns in shapes or arrangements

Real-life Applications:

Solving Sudoku and crosswords
Coding and programming logic
Weather prediction patterns
Stock market trend analysis
Game strategies (chess, checkers)

Solved Examples

Worked Example

Find the next three terms in the sequence: 4, 9, 16, 25, ...

Solution

Step 1: Observe the sequence: 4, 9, 16, 25
Step 2: Recognize these as squares: 2²=4, 3²=9, 4²=16, 5²=25
Step 3: Pattern: squares of consecutive integers starting from 2
Step 4: Next terms: 6²=36, 7²=49, 8²=64

Answer: 36, 49, 64

Worked Example

Find the missing number in the sequence: 3, 6, 11, 18, ?, 38

Solution

Step 1: Find differences between consecutive terms:
Step 2: 6 - 3 = 3
Step 3: 11 - 6 = 5
Step 4: 18 - 11 = 7
Step 5: Differences increase by 2 each time: 3, 5, 7, 9, 11
Step 6: Next difference should be 9
Step 7: Missing number = 18 + 9 = 27
Step 8: Check: 27 + 11 = 38 ✓

Answer: Missing number = 27

Worked Example

Solve the puzzle: If 2 + 3 = 10, 4 + 5 = 36, 6 + 7 = 78, then 8 + 9 = ?

Solution

Step 1: Look for the operation pattern:
Step 2: 2 + 3 = 5, but answer is 10 → 5 × 2 = 10
Step 3: 4 + 5 = 9, answer is 36 → 9 × 4 = 36
Step 4: 6 + 7 = 13, answer is 78 → 13 × 6 = 78
Step 5: Pattern: (a + b) × a = result
Step 6: For 8 + 9: sum = 17, then 17 × 8 = 136

Answer: 8 + 9 = 136

Key Points

Logical sequences follow a hidden rule or pattern
Check differences between terms for arithmetic patterns
Check ratios between terms for geometric patterns
Look for alternating sequences (odd/even positions)
Recognize special sequences: squares, cubes, primes, Fibonacci
For puzzles, test different operations (+, -, ×, ÷) systematically
Sometimes the pattern uses position numbers, not just previous terms

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.A logical sequence follows a:

Explanation: A fixed rule.

Q2.The next term of $2, 4, 6, 8$ is:

Explanation: Add $2$.

Q3.The next term of $3, 9, 27$ is:

Explanation: Multiply by $3$.

Q4.The next term of $1, 4, 9, 16$ is:

Explanation: Square numbers.

Practice more MCQs → 📝 Assignment · 35 marks