Rice on the Chessboard

By Math Is Fun, July 18, 2021

My son is a pretty big chess fan. So he was delighted when I told him this story.

Legend has it that chess was invented by Sissa from India. He presented his new creation to the king, who was highly entertained by the game and offered Sissa a gift. The king allowed Sissa to choose his own reward.

Sissa made a modest request for his gift. He asked for a single grain of rice on the first square of the chessboard, two grains on the second square, four grains on the third square, and so on. The number of grains would double each time until the final square was reached.

My son chimed in, “There are 8 rows and 8 columns on a chessboard.”

“That’s right,” I replied. “And how many squares does that make?” 

“8 by 8, 64!” my son answered confidently.

“Exactly,” I continued with the story. “The king was surprised by Sissa’s modest request. He granted it without much hesitation. Do you know what happened next?” I asked. 

“Did Sissa receive his gift?”

“Can you try to calculate the amount of rice Sissa is entitled to?” I asked.

Son grabbed a sheet of paper and began his computation. As he reached the 25th square, he exclaimed, “The number is growing very large, very quickly!” For the 25th square, the number stood at 16,777,216 – that’s 16 million.

“I should mention that there is a quicker method to calculate the total quantity of rice. It’s a little complex for you.” I added. “However, I can tell you the precise figure, which is 18,446,744,073,709,551,615.” I wrote the number on the sheet of paper.

Son began to count the commas in the number, “That’s thousand, million, billion….”

“It’s 18 quintillion!” I said. “Do you know how massive that number is?”

“At present, the global rice production amounts to 500 million tons annually, which equals 500 billion kilograms. Each kilogram comprises approximately 50,000 grains of rice. Therefore, 18 quintillion grains of rice surpasses the entire world rice output for over 737 years!” I explained.

“Wow! I suppose the request for the gift is not as simple as it seemed,” my son exclaimed.

“Correct. It’s a pledge the king cannot possibly fulfill,” I responded.

Power of the numbers

The takeaway of the story is that numbers are magical and powerful. Math is the tool to harness this power.

Also don’t promise a gift you cannot afford!