Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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

(5 pont)

Deadline expired on December 10, 2014.

### Statistics:

 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.

Problems in Mathematics of KöMaL, November 2014