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There are a total of 7 tables in the classroom, each seating 4 students, so the total number of students that can sit at the tables is 7 tables * 4 students per table = <<7*4=28>>28 students.
Therefore, the number of students that cannot sit down at the tables is 29 students - 28 students = <<29-28=1>>1 student. Answer: \boxed{1}.