The Farmer and the Three Sons Puzzle is a famous logic and math riddle that teaches the value of creative problem-solving. It begins with a farmer who owns 17 horses and wants to divide them among his three sons according to specific fractions. However, when you do the math, 17 doesn’t divide evenly according to those shares.

This puzzle is widely used in reasoning tests, interviews, and math competitions. It’s a perfect example of thinking outside the box, solving a problem that seems impossible at first glance.

The Farmer and Three Sons Puzzle Setup and Rules

Here’s how the puzzle is presented:

• A farmer owns 17 horses.
• He wants to divide them among his three sons as follows:
  • First son: half of the horses.
  • Second son: one-third of the horses.
  • Third son: one-ninth of the horses.
• The farmer insists that no horse be divided or harmed in the process.

The problem:
How can the farmer divide 17 horses according to these fractions without splitting any horse?

Objective

The goal is to figure out a fair and accurate way to divide the 17 horses among the three sons, following the father’s wish - ½, ⅓, and 1⁄9 - all while keeping the total count intact.

This requires logical thinking and a clever mathematical twist.

Step-by-Step Solution for The Farmer and the Three Sons Puzzle

The magic lies in a simple yet brilliant trick, temporarily adding one horse to make the division possible. Let’s walk through it step by step.

Step 1: Add an Extra Horse

To make the division easier, imagine that the farmer borrows one horse from a neighbor.

Now, the total number of horses becomes 18 instead of 17.
This small change makes the math work perfectly while still allowing the farmer to return the borrowed horse later.

Step 2: Divide the Horses

Now the division follows the farmer’s instructions exactly:

• First son: gets ½ of 18 = 9 horses
• Second son: gets ⅓ of 18 = 6 horses
• Third son: gets 1⁄9 of 18 = 2 horses

Step 3: Verify the Total

Let’s add them all up:

9 (first son) + 6 (second son) + 2 (third son) = 17 horses

That’s exactly the number of horses the farmer originally owned.
The extra horse was only a temporary helper to make the math work.

Step 4: Return the Borrowed Horse

After completing the division, the extra horse is returned to its owner.
Every son receives the exact portion their father wanted, and no horse was divided or harmed.

Final Answer:

Here’s how the horses are finally distributed:

Son	Fraction of Horses	Horses Received
First Son	½ of 18	9
Second Son	⅓ of 18	6
Third Son	1⁄9 of 18	2

Total = 17 horses distributed
1 borrowed horse returned

Thus, the puzzle is solved neatly, and everyone gets their fair share.

Explanation Behind the Trick

This puzzle demonstrates the power of creative logical reasoning.
At first, the problem looks mathematically impossible because the fractions of 17 don’t add up cleanly. However, by temporarily changing the perspective, adding an imaginary or borrowed horse, the math becomes possible.

When calculated with 18 horses:

12+13+19=9+6+218=1718\frac{1}{2} + \frac{1}{3} + \frac{1}{9} = \frac{9 + 6 + 2}{18} = \frac{17}{18}21​+31​+91​=189+6+2​=1817​

That means only 17 of the 18 horses are used in the distribution, leaving one extra horse to return.

This clever use of arithmetic logic is why this puzzle is a timeless favourite.

Why is the Farmer and Three Sons Puzzle is Popular?

This riddle is more than a math trick; it’s a lesson in creative problem-solving.
It shows how a small shift in approach can turn an impossible situation into a perfect solution.

The puzzle is often used in:

• Aptitude and reasoning exams
• Job interviews (especially in logical thinking tests)
• Educational math challenges and riddles

It’s a great exercise in lateral thinking, using imagination to solve problems that strict calculation alone can’t fix.

Similar Logic Puzzles with Answers

If you liked the Farmer and the Three Sons Puzzle, here are more classic logic puzzles that test creativity and reasoning.

1. The 100 Prisoners Hat Puzzle – Using Parity Logic

Setup: 100 prisoners must guess their hat colors using a shared logical strategy.
Answer: With the parity method, 99 survive for sure, and sometimes all 100.

2. The River Crossing Puzzle – The Goat, Wolf, and Cabbage

Setup: A farmer must take a goat, wolf, and cabbage across a river without losing any.
Answer: By taking the goat first, then the wolf, then the cabbage, the farmer safely crosses all.

3. The Two Doors Riddle – Truth and Lies

Setup: Two guards guard two doors: one leads to freedom, one to death.
Answer: Ask either guard, “If I asked the other which door leads to safety, what would he say?” Then choose the opposite door.

4. The Monty Hall Problem – Probability and Choice

Setup: You pick one of three doors. Behind one is a car; the others hide goats.
Answer: Always switch. The probability of winning doubles from 1/3 to ⅔.

5. The Camel and Bananas Puzzle – Desert Transportation Trick

Setup: A camel can only carry a certain number of bananas across the desert and eats as it walks.
Answer: The key is strategic loading and unloading to maximize how many bananas reach the destination.