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    • People at a Dinner party

      Party people

      1 January, 2005
      January 2005


      Friends or strangers?

      Friends or strangers?

       

       

      Is it possible to hold a party at which no two people have the same number of friends as each other?



      If you are stumped by last issue's puzzle, here is the solution.

      For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

      Solution link
      Party people solution
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      Anonymous

      18 May 2011

      Permalink
      Comment

      This is a great question. Without giving away the answer ( if you don't have it yet avert your eyes), the question is solvable using graph theory.

      Let each person at the party be a vertex. Form an edge between two people if they are friends. Now think about using the pigeon-hole principle.

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