A farmer is getting old and wants to divide his farm among his three sons. The farm consists of 17 horses. The farmer wants to distribute the horses in the following way:

• The first son should receive half of the horses.
• The second son should receive one-third of the horses.
• The third son should receive one-ninth of the horses.

The challenge is that 17 horses cannot be divided evenly according to these fractions. The question is: How can the farmer divide the horses among his three sons according to his wishes without splitting any horse?

Objective:
Determine how the farmer can fairly and accurately divide the 17 horses among his three sons according to the specified fractions.

Solution

The key to solving this puzzle lies in a clever trick that involves temporarily increasing the number of horses to make the division possible.

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

Step 1: Add an Extra Horse

To solve the problem, imagine that the farmer borrows one additional horse, temporarily increasing the total number of horses to 18. This extra horse makes it possible to divide the horses according to the required fractions.

Step 2: Distribute the Horses

Now, divide the 18 horses according to the farmer's wishes:

• First Son: Half of 18 horses is 9 horses.
• Second Son: One-third of 18 horses is 6 horses.
• Third Son: One-ninth of 18 horses is 2 horses.

Step 3: Calculate the Total

Adding up the horses distributed to the sons:

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

This leaves the 1 extra horse that was borrowed, which can now be returned.

Step 4: Return the Extra Horse

After the division, the borrowed horse is returned, and the distribution is complete. Each son receives the correct number of horses, and the total remains 17, with no horses split.

Final Answer

The farmer can divide the 17 horses among his three sons as follows:

• The first son receives 9 horses.
• The second son receives 6 horses.
• The third son receives 2 horses.

This division is achieved by temporarily adding an extra horse, making the fractions work out perfectly.