MMO 355 Moscow MO 1957 student uses subway and tram, money
Source:
August 20, 2019
algebranumber theory
Problem Statement
a) A student takes a subway to an Olympiad, pays one ruble and gets his change. Prove that if he takes a tram (street car) on his way home, he will have enough coins to pay the fare without change.
b) A student is going to a club. (S)he takes a tram, pays one ruble and gets the change. Prove that on the way back by a tram (s)he will be able to pay the fare without any need to change.Note: In , the price of a subway ticket was kopeks, that of a tram ticket kopeks, the denominations of the coins were , and kopeks. ( rouble = kopeks.)