A corollary that provides seat arrangements for even numbers of seats

Abstract

Let 1, 2, 3,..., n be n students and s1, s2, s3,..., sn be n row seats. A seat is arranged for each student on each day of the following n days. It is required that each student shall have different seat every day of the n days. Also, it is required that for these n day every student shall have a chance to sit next to every other student on one of his side and shall have another chance to sit next to every other student on the other of his side. In this paper, it is shown that such arrangements are possible when the number of students is even. Also, an algorithm for such arrangements is provided.