Can You Solve This Math Olympiad Riddle for Kids?

 

🧠 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 $a, b, c$ such that

$$a \times b \times c = 36.$$

The prime factorization of 36 is $2\times 2\times 3\times 3$.
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:

• (1, 6, 6)

• (2, 2, 9)

---

Step 3: Use logic to break the tie

If you were told, “The oldest sibling loves chess,” what would that mean?

• In (1, 6, 6), there are two oldest siblings (the twins, both 6).

• 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:

• practicing factors and multiplication,

• introducing systematic listing, and

• 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!

Solving Problems Involving Proportions and Percent

 

Proportions and percentages are everywhere: sales discounts, population growth, test scores, even restaurant tips. Understanding how to connect proportions with percent unlocks the ability to make quick, accurate decisions in everyday life.

---

What is a Proportion?

A proportion is an equation showing that two ratios are equivalent.

Example:

$$\frac{2}{5} = \frac{8}{20}$$

This proportion says “2 out of 5 is the same as 8 out of 20.”

---

What is Percent?

The word “percent” means “per hundred.”

• 45% = 45 out of 100 = $\frac{45}{100}$.

• Percentages are just special ratios with a denominator of 100.

---

Example 1: Shopping Discount

A jacket costs $80, and the store offers a 25% discount. How much will you save?

Set up proportion:

$$\frac{25}{100} = \frac{x}{80}$$

Cross multiply:

$$100x = 25 \times 80 \implies x = 20$$

💡 Answer: You save $20. Final price = $60.

---

Example 2: Exam Score

You answered 42 questions correctly out of 50 total questions. What percent is that?

$$\frac{42}{50} = \frac{x}{100}$$

Cross multiply:

$$50x = 4200 \implies x = 84$$

💡 Result: You scored 84%.

---

Example 3: Recipe Adjustment

A recipe needs 3 cups of flour to make 24 cookies. How many cups are needed for 40 cookies?

$$\frac{3}{24} = \frac{x}{40}$$

Cross multiply:

$$24x = 120 \implies x = 5$$

💡 Answer: Use 5 cups of flour.

This problem doesn’t mention percent directly, but it uses proportions in the same way.

---

Example 4: Population Growth

A town had 12,000 people last year. This year, the population grew by 15%. What’s the new population?

Find 15% of 12,000:

$$\frac{15}{100} \times 12,000 = 1,800$$

New population = 12,000 + 1,800 = 13,800 people.

---

Why Proportions and Percents Work Together

• Proportions let you scale relationships fairly.

• Percents let you quickly compare parts of 100.

• Together, they create a flexible toolkit for solving real-world problems.

---

Quick Strategy Guide

1. Write a ratio (part/whole).

2. Set it equal to $x/100$ (for percent problems).

3. Use cross multiplication or scaling to solve.

---

✅ Key Takeaways

• Proportions are equal ratios, and percent is just “out of 100.”

• Many real-life problems (sales, grades, cooking, growth) boil down to solving proportions.

• Once you see the pattern, percent problems become simple proportional reasoning.