Two travellers were walking along a dusty road. One carried three loaves of bread. The other carried two.
As the sun grew warm, they came to a well with a large, shady tree beside it. They decided to rest and eat their bread together.
Just as they began to eat, a third traveller arrived. He had no bread, but he looked tired and hungry.
“Will you share your meal with me?” he asked.
The two travellers nodded. They spread all five loaves on a clean cloth and shared them equally among the three of them.
When the meal was finished, the third traveller bowed and said, “I have no bread to give you — but I want to thank you.”
He placed five gold coins on the cloth.
“Please divide this between you, as a sign of my gratitude.”
And then he went on his way.
The two travellers looked at the coins.
“We should divide them in a 3 to 2 ratio,” said the one who had brought three loaves. “That is what we brought.”
“No,” said the other. “We shared our bread equally. We should divide the coins equally — half each.”
They could not agree.
So they went to a wise judge and told him the whole story.
The judge listened carefully. Then he said:
“The fair division is not 3 to 2, and not half and half. The first traveller should receive four coins. The second traveller should receive one coin.”
🧩 What do you think?
How did the judge reach this conclusion?
Hint: Think about how much bread each traveller actually gave to the stranger — not how much they had.
💡 The Unfolding
Let us see what the judge saw.
There were five loaves in total.
Three travellers shared them equally, so each person ate:
\( \frac{5}{3} \) loaves.
The traveller with three loaves gave away:
\( 3 - \frac{5}{3} = \frac{4}{3} \) loaves
The traveller with two loaves gave away:
\( 2 - \frac{5}{3} = \frac{1}{3} \) loaves
So the bread that was shared with the stranger came in a 4:1 ratio.
Therefore, the five coins should be divided in that same ratio:
- — The first traveller receives 4 coins
- — The second traveller receives 1 coin
And that is why the judge ruled as he did.
Sometimes, fairness is not about what we have — but about what we give.
The End