Problem B. 4660. (November 2014)
B. 4660. In a championship, every team plays every other team exactly once. 3 points are awarded for winning, 0 for losing, and 1 for a draw. In the case of equal scores, the order of the teams is determined at random. The championship is in progress at the moment. Team \(\displaystyle A\) is leading the points table. If team \(\displaystyle A\) scores exactly \(\displaystyle x\) points in the remaining rounds then they will win the championship. However, if \(\displaystyle A\) scores more than \(\displaystyle x\) points, they will not necessarily win. (It is possible for \(\displaystyle A\) to score more than \(\displaystyle x\).) How many rounds remain to be played in the championship?
Suggested by V. Vígh, Szeged
Deadline expired on December 10, 2014.
57 students sent a solution. 5 points: Baran Zsuzsanna, Bereczki Zoltán, Cseh Viktor, Csorba Benjámin, Czirkos Angéla, Éles Márton, Geng Máté, Hansel Soma, Horeftos Leon, Horváth Miklós Zsigmond, Katona Dániel, Lajkó Kálmán, Márki-Zay Anna, Mikulás Zsófia, Mócsy Miklós, Nagy Kartal, Nagy-György Pál, Schwarcz Tamás, Szakály Marcell, Szebellédi Márton, Temesi András, Tóth Viktor, Zolomy Kristóf. 4 points: Bencze Tamás, Cseh Kristóf, Imolay András, Kátay Tamás, Keresztfalvi Bálint, Leitereg Miklós, Molnár 410 Roland, Molnár-Sáska Zoltán, Olexó Gergely, Szajbély Zsigmond, Vágó Ákos, Váli Benedek, Williams Kada. 3 points: 7 students. 2 points: 8 students. 1 point: 2 students. 0 point: 1 student. Unfair, not evaluated: 3 solutions.