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Problem of the Month – December 2020

Let N be the total number of bijective functions
f : {1, 2, . . . , 2020} → {1, 2, . . . , 2020}
satisfying (((k))) = k for all k = 1, 2, . . . , 2020. Show that N is divisible by 3336 .

 

 

Correct Solutions by,

  • Toshihiro Shimizu Kawasaki, Japan
  • Chui Tsz Fung, Hong Kong
  • Steffen Weber, Ismaning, Germany
  • Albert Stadler, Herrliberg, Switzerland
  • İbrahim Berkay Ceylan, Giresun Fen Lisesi
  • Jepbar Asgarov, Hitrowka, Turkmenistan
  • Tan Özalp, Orta Doğu Teknik Üniversitesi, Ankara
  • Magnus Jakobsson, Lund, Sweden
  • Muhammed İkbal Ulvi, Orta Doğu Teknik Üniversitesi, Ankara
  • Kadyr Annabayev, Turkmen State Institute of Architecture and Construction, Turkmenistan
  • Roger Bengtsson, Lund, Sweden
  • Cüneyd Öztürk, Bilkent Üniversitesi
  • Omar Sonebi, Lycee technique Settat, Casablanca, Morocco
  • Enes Kocabey, Google, Mountain View, USA
  • Kipp Johnson, Oregon, USA

Solution: http://www.fen.bilkent.edu.tr/~cvmath/Soru/2011c.pdf