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Answer :
This process continues, halving the correlation remaining range after each guess until you find the exact amount.
Since the range of possible amounts is from $1 to $2,000, you can start by guessing the midpoint of this range, which is $1,000. If the man tells you that your guess is too high, you can narrow down the range to $1 to $999 and repeat the process.
In this case, your next guess should be the midpoint of the new range, which is $500. If the man tells you that your guess is too low, you can narrow down the range to $501 to $999 and guess the midpoint again. This process continues, halving the remaining range after each guess until you find the exact amount.
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