Problem B. 4757. (December 2015)
B. 4757. Let \(\displaystyle A_k\) denote the number that consists of \(\displaystyle k\) ones in decimal notation. How many positive integers are there that cannot be obtained as the sum of the digits of any multiple of \(\displaystyle A_k\)?
Proposed by K. Williams, Szeged
Deadline expired on January 11, 2016.
39 students sent a solution. 6 points: Baran Zsuzsanna, Borbényi Márton, Bukva Balázs, Csorba Benjámin, Czirkos Angéla, Döbröntei Dávid Bence, Gáspár Attila, Imolay András, Klász Viktória, Kovács 246 Benedek, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Nagy Kartal, Tóth Viktor. 5 points: Lajkó Kálmán, Matolcsi Dávid, Várkonyi Dorka. 4 points: 4 students. 3 points: 2 students. 2 points: 1 student. 1 point: 7 students. 0 point: 8 students.