Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 503. (March 2016)

K. 503. A mathematics teacher was having fun on the 1st of April. During that day, he interpreted any written numbers and operations as representations in the base equal to the whole hour of the time instant the operation was carried out. (For example, at 32 minutes past 1 p.m., that is, at 13:32, he assumed that numbers were represented in base 13.) When he first carried out a multiplication, he got 181 as a result. One hour later, he carried out the multiplication written down with the very same digits, and got 180. Two additional hours after the second multiplication, he added the numbers 180 and 181, and obtained 341. What was the original multiplication (written down with the original digits)?

(6 pont)

Deadline expired on April 11, 2016.

### Statistics:

 55 students sent a solution. 6 points: Barta Ákos, Bertók Zsanett, Bognár Ádám, Csáfordi József, Dékány Barnabás, Dobák Dániel, Fekete Barnabás, Gilicze Márton, Hoffmann Balázs, Jankovits András, Keltai Dóra, Kluèka Vivien, Köpenczei Csenge, Máté 446 Dávid, Mészáros 916 Márton, Nyitrai Boglárka, Pinke Jakab Zoltán, Rubovszky Cecília , Ruzsa Kata, Sal Dávid, Simon Dóra, Varga 294 Ákos, Vida Kata. 5 points: Csóka Zoárd, Debreczeni Tibor, Földvári Ádám, Gárdonyi Csilla Dóra, Gortka Bence, Kertész Ferenc, Kiss 468 Péter, Koltai Dániel, Kovács 161 Márton Soma, Marshall Tamás, Mester Gyöngyvér, Mónos Péter, Nagy Csaba Jenő, Pálvölgyi Szilveszter, Póta Balázs, Vitányi Borbála. 4 points: 6 students. 3 points: 2 students. 2 points: 5 students. 1 point: 2 students. 0 point: 1 student.

Problems in Mathematics of KöMaL, March 2016