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jmc

counting and probability junior

Problem

There are seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
(A)
(B)
(C)
(D)
Solution
Let be a person seated and is an empty seat The pattern of seating that results in the fewest occupied seats is . We can group the seats in 3s like this: There are a total of groups
Final answer
B