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Problem of the Month – October 2022

Each of n guests at a party wears a hat of one of three colours. A guest is said to be
lucky if at least two of its friends in the party wear differently coloured hats. Find all values
of n for which it is always possible to choose a guest and to change its hat to hat of one
of the remaining two colours such that the total number of lucky guests will not be decreased.


Correct Solutions by,

  • Toshihiro Shimizu Kawasaki, Japan
  • Serdar Hojayev Dashoguz, Turkmenistan
  • Mehmet Sarak İstanbul Bahçeşehir Fen ve Teknoloji Lisesi
  • Mustafa Burak Topal İstanbul


Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/2210a.pdf