The Chessboard and the Rice
Written by Studio AM.
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A quantity can grow by adding the same amount at each step or by multiplying by the same factor. Starting at one and adding one gives one, two, three, four. Doubling instead gives one, two, four, eight. Both sequences begin with small numbers, but their later values are very different.
An old chessboard story illustrates the difference. A ruler offers a reward, and someone asks for grains of rice: one on the first square, two on the second, four on the third, doubling across all sixty-four. By the eleventh square, that square alone requires 1,024 grains. The sixty-fourth requires more than nine quintillion. The small starting amount is misleading if intuition replaces calculation.
Repeated doubling is one example of exponential growth. A fixed percentage increase also compounds, though it does not necessarily double at every step. The extra amount grows because the percentage applies to an increasingly large total. For example, a ten percent increase adds ten to one hundred but twenty to two hundred.
The chessboard follows a mathematical rule. Real technologies and populations need not keep that rule indefinitely: resources, demand and other conditions can limit growth. A useful forecast therefore asks both how quickly a quantity is changing and whether that rate is likely to continue. An overwhelming total calculated from repeated doubling shows what the assumption implies, not a promise that the world will follow it.
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Question 1 of 4
What is the passage mainly about?
The answer is A: Repeated multiplication can produce large totals, but real forecasts must test the growth assumption.
The rice sequence demonstrates repeated doubling. The final paragraph distinguishes that exact mathematical rule from uncertain real-world growth.
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Question 2 of 4
In the chessboard story, how does the amount of rice change from one square to the next?
The answer is B: It doubles on each square
The courtier asks for rice 'doubling across all sixty-four' squares.
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Question 3 of 4
Why would the chessboard rule alone be insufficient to forecast a real population?
The answer is A: Resources and other conditions may prevent the assumed rate from continuing.
The final paragraph says resources and other conditions can limit growth, so the rate must be assessed rather than assumed permanent.
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Question 4 of 4
What does 'intuition' mean in this passage?
The answer is A: an immediate gut sense
The sentence contrasts an immediate sense of the amount with calculating the doubling sequence.
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