Age Product Puzzle
Age Product Puzzles are classic problems where the product of ages is given along with the sum, and additional clues (like 'oldest has red hair') help determine the unique solution. These puzzles test factor analysis and logical elimination.
What You'll Learn
Introduction to Age Product Puzzle
Age Product Puzzles are classic problems where the product of ages is given along with the sum, and additional clues (like 'oldest has red hair') help determine the unique solution. These puzzles test factor analysis and logical elimination.
Prerequisites
How to Solve Age Product Puzzle Problems
Step 1: Write the product equation (e.g., A × B × C = P)
Step 2: List all possible factor triples (ages)
Step 3: Calculate sum for each triple
Step 4: If sum is known but ambiguous, identify triples with same sum
Step 5: Use additional clue (oldest/youngest/twins) to resolve ambiguity
Step 6: Select the unique solution
Step 7: Verify all conditions
Example Problem
Example: Product of three children's ages is 72. Sum is the house number. The oldest likes ice cream. Find ages. Solution: Factor triples of 72: (1,1,72) sum=74, (1,2,36) sum=39, (1,3,24) sum=28, (1,4,18) sum=23, (1,6,12) sum=19, (1,8,9) sum=18, (2,2,18) sum=22, (2,3,12) sum=17, (2,4,9) sum=15, (2,6,6) sum=14, (3,3,8) sum=14, (3,4,6) sum=13, (4,4,4.5) invalid. Only (2,6,6) and (3,3,8) have same sum=14. 'Oldest' implies unique oldest, so (3,3,8) has oldest 8, (2,6,6) has two oldest (twins) → choose (3,3,8). Answer: Ages are 3, 3, and 8
Pro Tips & Tricks
- Ages are typically positive integers for children
- List triples with ages in non-decreasing order
- Twins = two ages equal
- Unique oldest = exactly one age greater than others
- The 'house number' clue indicates the sum is ambiguous
- Additional clues often involve physical characteristics
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Age Product Puzzle. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Age Product Puzzle is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Age Product Puzzle?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: