Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem B. 4781. (March 2016)

B. 4781. The rows and the columns of an $\displaystyle n \times n$ chessboard are numbered 1 to $\displaystyle n$, and a coin is placed on each field. The following game is played: A coin showing tails is selected. If it is in row $\displaystyle k$ and column $\displaystyle m$, then every coin with row number at least $\displaystyle k$ and column number at least $\displaystyle m$ is turned over. This procedure is repeated.

What is the least number $\displaystyle L(n)$ for which it is possible to achieve in at most $\displaystyle L(n)$ steps that all coins on the board show heads, whatever be the initial distribution of heads and tails?

Proposed by D. Lenger, J. Szoldatics, Budapest

(6 pont)

Deadline expired on April 11, 2016.

### Statistics:

 68 students sent a solution. 6 points: Alexy Milán, Andó Angelika, Baran Zsuzsanna, Bindics Boldizsár, Bodolai Előd, Bukva Balázs, Busa 423 Máté, Csorba Benjámin, Döbröntei Dávid Bence, Fuisz Gábor, Gáspár Attila, Győrffy Ágoston, Hansel Soma, Hraboczki Attila Márton, Imolay András, Kerekes Anna, Keresztfalvi Bálint, Klász Viktória, Kovács 162 Viktória, Kovács 246 Benedek, Kőrösi Ákos, Kuchár Zsolt, Lajkó Kálmán, Lajos Hanka, Lakatos Ádám, Márton Dénes, Matolcsi Dávid, Molnár Bálint, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Nagy Kartal, Németh 123 Balázs, Nguyen Viet Hung, Polgár Márton, Saár Patrik, Schrettner Jakab, Somogyi Pál, Souly Alexandra, Sudár Ákos, Szabó 417 Dávid, Szabó Kristóf, Szakály Marcell, Tiszay Ádám, Tóth Viktor, Tran 444 Ádám, Vágó Ákos, Váli Benedek, Vári-Kakas Andor, Weisz Máté, Zólomy Kristóf. 5 points: 10 students. 4 points: 1 student. 3 points: 5 students. 0 point: 2 students.

Problems in Mathematics of KöMaL, March 2016