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Omni-MATH / In a classroom, 34 students are seated in 5 rows of 7 chairs. The place at the…

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problem

In a classroom, 34 students are seated in 5 rows of 7 chairs. The place at the center of the room is unoccupied. A teacher decides to reassign the seats such that each student will occupy a chair adjacent to his/her present one (i.e. move one desk forward, back, left or right). In how many ways can this reassignment be made?

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