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Let the guessed value be x.

Actual number of beans = 645

Maximum difference allowed between guessed number and actual number = 20

So, the maximum guess is

645 + 20 = 665

645 = 665 - 20

Replace 665 with x since it is the guessed value

645 = x - 20

20 = x - 645

x - 645 = 20 ---(1)

Minimum guess is

645 - 20 = 625

645 = 625 + 20

645 = x + 20

645 - x = 20

-(x - 645) = 20 ---(2)

Combining equations (1) and (2) we get

|x - 645| = 20

So, the above equation can be used to find the minimum and maximum number of beans that will win the contest.

ANSWER: |x - 645| = 20 ; maximum guess 665 beans

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