🧠 Introduction
Math Olympiad problems aren’t just about numbers — they’re about thinking creatively.
Here’s a fun Olympiad-style puzzle for elementary students that tests reasoning, logic, and number sense. See if you can solve it before peeking at the solution!
❓ The Problem
Three siblings have whole-number ages.
The product of their ages is 36, and the sum of their ages is 13.
Can you find out how old the siblings are?
(Bonus: If there’s more than one possible answer, what extra clue might help you decide?)
🧩 Step-by-Step Solution
Step 1: Find all possible triples of ages
We’re looking for whole numbers such that
The prime factorization of 36 is .
Let’s group them into triples (order doesn’t matter):
| Possible Ages | Sum |
|---|---|
| 1, 1, 36 | 38 |
| 1, 2, 18 | 21 |
| 1, 3, 12 | 16 |
| 1, 4, 9 | 14 |
| 1, 6, 6 | 13 |
| 2, 2, 9 | 13 |
| 2, 3, 6 | 11 |
| 3, 3, 4 | 10 |
Step 2: Use the sum condition
We’re told the sum is 13, so there are two possibilities:
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(1, 6, 6)
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(2, 2, 9)
Step 3: Use logic to break the tie
If you were told, “The oldest sibling loves chess,” what would that mean?
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In (1, 6, 6), there are two oldest siblings (the twins, both 6).
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In (2, 2, 9), there is one unique oldest sibling (the 9-year-old).
So the final answer must be: 2, 2, 9
✅ Final Answer
The siblings are 2 years, 2 years, and 9 years old.
💡 Teaching Tip (for educators or parents)
This puzzle is great for:
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practicing factors and multiplication,
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introducing systematic listing, and
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encouraging logical reasoning.
Try modifying the product (e.g. 24, 48, or 60) to create new challenges!
🏁 Conclusion
Math Olympiad problems like this show that logic and creativity are just as important as calculation. Encourage students to think about patterns and test their ideas — that’s what real problem-solving is all about!