Question 124
in a boarding school, $512$ Students Learn $9$ Disciplines. these students live in $256$ Double Rooms; two students are called *neighbors* if they share a room. It is known that for every two students the sets of disciplines in which they are interested in nothing). prove that all the students can be arranged in a circle so that Adjacent students, one of them is interesting in all the disciplines Interested in exactly one additional discipline. The boarding school is taught $9$ subjects and learn $512$ children settled in $256$ double rooms (children living in the same room, let's call *neighbors*). It is known that any two children have different sets of objects that are interesting to them (in particular, exactly one child is not interested in anything). Prove that all children can be built in a circle so that any two neighbors stand side by side, and for any two non-neighbors standing nearby, one of them is interested in all objects that are interesting to another, and exactly one more object.