Let N be the total number of bijective functions
f : {1, 2, . . . , 2020} → {1, 2, . . . , 2020}
satisfying f (f (f (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