5
Part of 1998 May Olympiad
Problems(2)
two types of tickets on planet X31
Source: IV May Olympiad (Olimpiada de Mayo) 1998 L2 P5
9/17/2022
On planet there are only two types of tickets, however the system is not so bad because there are only fifteen full prices that cannot be paid exactly (you pay more and receive change). If is one of those prices that cannot be paid exactly, find the value of each type of bill.
number theory
list of 21 different numbers related to 4-digit no
Source: IV May Olympiad (Olimpiada de Mayo) 1998 L1 P5
9/17/2022
Choose a four-digit number (none of them zero) and, starting with it, build a list of different numbers, each with four digits, that satisfies the following rule: after writing each new number in the list, all the averages are calculated Between two digits of that number, those averages that do not give a whole number are discarded, and with the rest a four-digit number is formed that will occupy the next place in the list. For example, if was written in the list, the next one can be or or or any other number armed with the figures , or .
number theory