The Ages of Daughters Puzzle is one of the most famous logic riddles that combines reasoning, mathematics, and deduction. In this puzzle, a man gives three clues about his daughters’ ages, and you must use logic to determine how old they are.

At first, it seems straightforward, but as you explore deeper, you realize it’s not just about math; it’s about interpreting hidden clues correctly. This puzzle is widely used in interview tests, IQ challenges, and logic-based games because it measures how well you can think critically and eliminate possibilities.

Ages of Daughters Puzzle Setup

Here’s how the puzzle is presented:

A man has three daughters, and someone asks him their ages.
He gives the following clues:

• The product of their ages is 36.
• The sum of their ages equals the house number next door.
• The oldest daughter has blue eyes.

Objective: Based on these clues, can you figure out the ages of the three daughters?

How to Solve the Ages of Daughters Puzzle?

This logic puzzle needs careful deduction. You have to use each clue step by step to narrow down the possible ages until only one combination fits perfectly.

Let’s break it down logically.

Step 1: Find All Possible Combinations

The first clue says the product of their ages is 36.
That means the three ages multiplied together must equal 36.

So, let’s list all the possible sets of ages that satisfy this condition:

Possible Ages	Product
1, 1, 36	36
1, 2, 18	36
1, 3, 12	36
1, 4, 9	36
1, 6, 6	36
2, 2, 9	36
2, 3, 6	36
3, 3, 4	36

All these sets work mathematically, but only one will match all three clues.

Step 2: Consider the Sum of the Ages

Now, the man says that the sum of their ages equals the house number next door.
We don’t know that number, but we can calculate the sum for each combination.

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

So now we know all possible sums.

Step 3: Analyze the Ambiguous Clue

The person asking the question still doesn’t know the answer after hearing the sum.
That means the sum must be ambiguous; in other words, it matches more than one possible combination.

Looking at our list, only the sum 13 appears twice.
Those combinations are:

• 1, 6, 6
• 2, 2, 9

So, the house number next door must be 13.

Step 4: Use the Final Clue About the Oldest Daughter

Now comes the third clue:

“The oldest daughter has blue eyes.”

This tells us that there is a single oldest daughter, not a tie between ages.

If we look at the combinations that sum to 13:

• In 1, 6, 6, there are two oldest daughters (both 6 years old).
• In 2, 2, 9, there is one distinct oldest daughter (age 9).

So, the only combination that makes sense is 2, 2, and 9.

Final Answer: Ages of the Three Daughters

The correct ages are 2, 2, and 9.

This fits all clues perfectly:

• Product = 2 × 2 × 9 = 36
• Sum = 13 (the house number)
• Oldest daughter = age 9 (blue eyes)

Step-by-Step Logic Summary:

Step	Clue	Deduction
1	Product = 36	List all combinations
2	Sum = House number	Narrow down based on sums
3	Ambiguity	Find repeated sum (13)
4	Oldest daughter	Choose the unique oldest (2, 2, 9)

Why the “Ages of Daughters” Puzzle Is Popular?

This puzzle is famous because it demonstrates how small clues can change everything. You might think math alone can solve it, but you also need logical reasoning and contextual understanding.

It’s used in:

• Tech and logical interviews
• IQ tests and Olympiads
• Brain teasers and logic puzzle books

The key takeaway: sometimes, math gives multiple possibilities, and you must use context to find the right one.

Similar Logic Puzzles with Answers

If you enjoyed this, here are more puzzles that test reasoning and deduction:

1. The 100 Prisoners Hat Puzzle

Setup: 100 prisoners must guess the color of their hats.
Answer: Using parity, at least 99 survive, sometimes all 100.

2. The River Crossing Puzzle

Setup: A farmer must get a wolf, goat, and cabbage across a river without anyone getting eaten.
Answer: Goat → Wolf → Cabbage → Goat again - all cross safely.

3. The Two Doors Riddle

Setup: Two guards, one always lies, one tells the truth. You can ask one question.
Answer: Ask, “What would the other guard say?” and pick the opposite door.

4. The Monty Hall Problem

Setup: Pick one of three doors - one has a car, others goats. The host opens a goat door.
Answer: Switching doubles your chance of winning.

5. The Blue Eyes Puzzle

Setup: On an island, no one knows their own eye color. A visitor reveals that one blue-eyed person exists.
Answer: If n people have blue eyes, all leave on the nth night.