A fair division storytale

While I was browsing random videos on Youtube, I came across an amusing story about fair division told by some Indian school children.

The video is about five minutes long and I found it enjoyable. And if the accents are throwing you off, you can read my transcription of the video written below.

Youtube video: Story – a fair division

My transcription of the story in the video

The title of the story is “A Fair Division.”

One very hot afternoon, two farmers, Ram and Shyam sat under the shade of a large tree. They had brought tasty chapatis [basically Indian tortillas] for lunch.

Ram had 3 pieces, and Shyam had 5. And they were about to begin their meal when a young nobleman rode by. “Good day, good sirs,” he said.

The nobleman looked tired and hungry. So Ram and Shyam invited the nobleman to share their food. “But, how are we supposed to divide these 8 chapatis among the 3 of us?” asked Ram.

“We shall stack up the chapatis and cut them into 3 equal parts,” suggested Shyam.

So they stacked up the chapatis and cut them into 3 equal parts. They ate the pieces equally so that no one ate more or less than anyone.

When they finished, the grateful nobleman insisted on paying for his share of food. He placed 8 gold coins into Ram’s palm.

“There are two of us, and 8 gold coins, so we should take 4 each,” suggested Ram.

“But that’s not fair,” argued Shyam, “I had 5 chapatis and you had only 3, so I should get 5 coins and you should get only 3.”

Ram did not want to quarrel, but he also did not want to give 5 of the coins to Shyam. “Let us go to the Maulvi [an expert in law],” suggested Ram, “he is always just.”

So Ram and Shyam went to the Maulvi’s house together. They told the Maulvi everything that had happened. The Maulvi thought for a long time. “The fair way to divide these 8 gold coins is to give 7 coins to Shyam and only 1 coin to Ram.”

“Huh? Why do I deserve only 1 gold coin,” argued Ram.

“And why do I deserve 7!?” said Shyam.

But when Maulvi explained his reasoning, both Ram and Shyam were satisfied that justice had been done.

Why was this a fair division?

Now, let’s see what the Maulvi’s explanation was.

How many chapatis were there in total? There were 8 in total.

If they were cut into 3 equal parts, how many pieces were there? There were 24 pieces.

Now how many chapati’s did Ram have? He had 3. If they were cut into 3 equal parts, then there were 9 pieces.

Now how many chapatis did Shyam have? He had 5, cut into 3 equal parts, making 15 pieces.

Now if there were 24 pieces in total, eaten equally, then each person had 8 pieces (24 divided by 3).

Out of the 9 pieces that Ram had, he ate 8 pieces himself, thus only 1 was for the guest.

Out of the 15 pieces Shyam had, he ate 8 pieces, and 7 pieces for the guest.

Thus Shyam deserves 7 gold coins (1 for each he gave the nobleman) and Ram deserves just 1 (for the 1 piece he gave the nobleman).

If Ram had been wiser and done the math himself, he might have accepted the generous offer of 3 gold coins and never suggested to visit the Maulvi.