Annoying Assignments

Professor Sundari wants to assign her 7 students group projects such that

  • nobody is doing a project all by themselves;
  • not everybody is doing the same project;
  • everybody is doing some project;
  • given any pair of people, there is exactly one project that they are both working on;
  • given any pair of projects, there is exactly one person who is working on both of them.

Can she give the assignment satisfying all these constraints?

Yes No

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