¶ 2026 AMC8 Problem 17
Problem:
Four students are seated in a row. They chat with the people sitting next to them, then rearrange themselves so that they are no longer seated next to any of the same people. How many rearrangements are possible?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Label the students as , and , from left to right. Notice that student is sitting next to students and and student is sitting next to students and . Therefore, the only way that the rearrangement with the given condition is possible is if student is sitting next to student and student is sitting next to student , which means that students and are at the ends of the row. There are ways to place the students at the ends, and since the placements of student and are locked afterwards, the answer is just .
The problems on this page are the property of the MAA's American Mathematics Competitions