Number Puzzles (Grade 4)
Number puzzles are fun challenges that use addition, subtraction, multiplication, and division to find missing numbers. They test your logical thinking and arithmetic skills at the same time.
In Class 4, you will solve puzzles like cross-number puzzles, missing-digit problems, number riddles, and input-output machines. These puzzles make maths exciting and sharpen your problem-solving ability.
What is Number Puzzles - Class 4 Maths (Patterns)?
A number puzzle is a problem where you use clues and mathematical operations to find unknown numbers. Types of number puzzles include:
- Missing digit puzzles: Find the digit that makes an equation true.
- Cross-number puzzles: Fill numbers in a grid where rows and columns satisfy given operations.
- Number riddles: A mystery number described by clues.
- Input-output machines: A rule transforms the input number into the output number.
Solved Examples
Example 1: Example 1: Missing digit in addition
Problem: Find the missing digit: 3_5 + 247 = 612
Solution:
Step 1: 3_5 + 247 = 612, so 3_5 = 612 − 247 = 365.
Step 2: The missing digit is 6.
Answer: The missing digit is 6. The number is 365.
Example 2: Example 2: Number riddle
Problem: I am a 2-digit number. My tens digit is 3 more than my ones digit. The sum of my digits is 9. What number am I?
Solution:
Step 1: Let ones digit = x. Then tens digit = x + 3.
Step 2: Sum: x + (x + 3) = 9 → 2x + 3 = 9 → 2x = 6 → x = 3.
Step 3: Ones digit = 3, Tens digit = 6.
Answer: The number is 63.
Example 3: Example 3: Input-output machine
Problem: An input-output machine gives: Input 5 → Output 13. Input 8 → Output 19. Input 12 → Output ?
Solution:
Step 1: Find the rule: 5→13: 5×2+3=13. 8→19: 8×2+3=19. Rule: multiply by 2 and add 3.
Step 2: Input 12: 12×2+3 = 24+3 = 27
Answer: Output = 27. Rule: ×2 + 3.
Example 4: Example 4: Missing digit in subtraction
Problem: Find ?: 8_3 − 456 = 397
Solution:
Step 1: 8_3 = 397 + 456 = 853
Step 2: The missing digit is 5.
Answer: The missing digit is 5. The number is 853.
Example 5: Example 5: Cross-number puzzle
Problem: Fill in the missing numbers so each row and column adds to the given sum.
| 5 | ? | → 12 |
| ? | 4 | → 10 |
| ↓ 11 | ↓ 11 |
Solution:
Step 1: Row 1: 5 + ? = 12 → ? = 7
Step 2: Column 1: 5 + ? = 11 → ? = 6
Step 3: Verify Row 2: 6 + 4 = 10 ✓ Column 2: 7 + 4 = 11 ✓
Answer: The missing numbers are 7 (top-right) and 6 (bottom-left).
Example 6: Example 6: Reverse operation puzzle
Problem: I think of a number, add 15, then double it. I get 46. What was my number?
Solution:
Step 1: Work backwards. Result = 46.
Step 2: Undo doubling: 46 ÷ 2 = 23
Step 3: Undo adding 15: 23 − 15 = 8
Answer: The number is 8. Check: 8 + 15 = 23, 23 × 2 = 46 ✓
Example 7: Example 7: Digit arrangement puzzle
Problem: Arrange the digits 3, 5, and 7 to make the largest possible 3-digit number and the smallest possible 3-digit number. Find their difference.
Solution:
Step 1: Largest: place digits in descending order → 753
Step 2: Smallest: place digits in ascending order → 357
Step 3: Difference: 753 − 357 = 396
Answer: Difference = 396.
Example 8: Example 8: Sum and difference puzzle
Problem: Two numbers add up to 50 and their difference is 14. Find the two numbers.
Solution:
Step 1: Larger number = (50 + 14) ÷ 2 = 64 ÷ 2 = 32
Step 2: Smaller number = 50 − 32 = 18
Step 3: Check: 32 + 18 = 50 ✓, 32 − 18 = 14 ✓
Answer: The numbers are 32 and 18.
Example 9: Example 9: Pattern-based puzzle
Problem: If 2 ★ 3 = 13 and 4 ★ 5 = 41, what is 3 ★ 6?
Solution:
Step 1: Find the rule: 2★3 = 2² + 3² = 4 + 9 = 13 ✓. 4★5 = 16 + 25 = 41 ✓.
Step 2: Rule: a ★ b = a² + b².
Step 3: 3 ★ 6 = 9 + 36 = 45
Answer: 3 ★ 6 = 45.
Example 10: Example 10: Multiplication missing digit
Problem: Find ?: _4 × 3 = 162
Solution:
Step 1: _4 × 3 = 162, so _4 = 162 ÷ 3 = 54.
Step 2: The missing digit is 5.
Answer: The missing digit is 5. The number is 54.
Key Points to Remember
- Number puzzles use logic and arithmetic to find missing numbers.
- For missing digit puzzles, use reverse operations (subtract to undo addition, divide to undo multiplication).
- For number riddles, translate clues into mathematical conditions and solve step by step.
- For input-output machines, test rules like +, −, ×, or combinations until one fits all given pairs.
- Working backwards is a powerful strategy: undo each operation in reverse order.
- Always verify your answer by plugging it back into the original puzzle.
- Cross-number puzzles require all rows AND columns to satisfy their conditions simultaneously.
Practice Problems
- Find the missing digit: 4_6 + 318 = 784
- I am a 2-digit number. My digits add up to 11. My tens digit is double my ones digit minus 1. What am I?
- Input-output: 3→11, 7→23, 10→? What is the rule?
- I think of a number, subtract 8, then multiply by 3. I get 27. What was my number?
- Two numbers add up to 100 and their difference is 24. Find them.
- Arrange digits 1, 6, 9 to make the largest and smallest 3-digit numbers. Find the difference.
- Find ?: _7 × 5 = 285
Frequently Asked Questions
Q1. What are number puzzles?
Number puzzles are mathematical problems where you use clues, logic, and arithmetic operations to find unknown numbers or digits. They include riddles, missing digit problems, and cross-number grids.
Q2. How do you solve missing digit problems?
Use the reverse operation. If the puzzle involves addition, subtract to find the missing number. If it involves multiplication, divide. Then identify the missing digit from the result.
Q3. What is working backwards?
Start from the final answer and reverse each step. Undo multiplication by dividing, undo addition by subtracting. This reveals the original number step by step.
Q4. How do you solve number riddles?
Convert each clue into a mathematical statement. For example, 'my tens digit is twice my ones digit' becomes T = 2 × O. Then solve the equations to find the number.
Q5. What is an input-output machine?
It is a puzzle where a rule transforms an input number into an output number. Given several input-output pairs, you figure out the rule and then apply it to new inputs.
Q6. How do you find the rule for an input-output machine?
Try simple operations first: is the output always the input plus a number? Times a number? A combination like ×2+1? Test your rule against all given pairs to confirm.
Q7. Can number puzzles have more than one answer?
Some puzzles can have multiple valid answers. However, most well-designed puzzles give enough clues for exactly one answer. If your answer is different, check all clues again.
Q8. How do number puzzles help with maths?
They build logical thinking, strengthen arithmetic skills, encourage creative problem-solving, and make practising operations more engaging than plain calculations.
