Question

In an old fable, a commoner who had saved the king's life was told he could ask the king for any just reward. Being a shrewd man, the commoner said, "A simple wish, sire. Place one grain of wheat on the first square of a chessboard, two grains on the second square, four grains on the third square, continuing until you have filled the board. This is all I seek." Compute the total number of grains needed to do this to see why the request, seemingly simple, could not be granted. (A chessboard consists of $8 \times 8=64$ squares.)

Name: Problem 95, Chapter 11: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-06-18T20:41:53-08:00
Duration: 2 min 19 s
Channel: Dale Sanford

   In an old fable, a commoner who had saved the king's life was told he could ask the king for any just reward. Being a shrewd man, the commoner said, "A simple wish, sire. Place one grain of wheat on the first square of a chessboard, two grains on the second square, four grains on the third square, continuing until you have filled the board. This is all I seek." Compute the total number of grains needed to do this to see why the request, seemingly simple, could not be granted. (A chessboard consists of $8 \times 8=64$ squares.)

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 11, Problem 95

Instant Answer

Solved by Expert Dale Sanford

06/18/2020

Step 1

The commoner requests that the number of grains of wheat on each square of the chessboard doubles from the previous square, starting with 1 grain on the first square. This means the number of grains on each square follows a geometric progression. Show more…

Show all steps

Thanks for your feedback!

In an old fable, a commoner who had saved the king's life was told he could ask the king for any just reward. Being a shrewd man, the commoner said, "A simple wish, sire. Place one grain of wheat on the first square of a chessboard, two grains on the second square, four grains on the third square, continuing until you have filled the board. This is all I seek." Compute the total number of grains needed to do this to see why the request, seemingly simple, could not be granted. (A chessboard consists of $8 \times 8=64$ squares.)

Play audio

Feedback

Dale Sanford and 72 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Exponential Growth

Exponential growth refers to the process by which a quantity increases by a fixed percentage or multiplicative factor over equal increments. In this context, doubling the number of grains on each successive square demonstrates how values can grow rapidly, highlighting the dramatic increase in the total even when starting from a seemingly small initial number.

Geometric Series

A geometric series is the sum of a sequence of terms where each term is a constant multiple of the previous one. This concept is used to calculate the total number of grains on the chessboard, as each square contains twice as many grains as the previous one. The sum of the series can be efficiently determined using the formula for the sum of a geometric series, giving insight into why the seemingly modest request is unfeasible.

Please give Ace some feedback