KöMaL 2010 K237

Customers at a parking lot are charged 120 forints (HUF, Hungarian currency) an hour for parking between 8 a.m. and 6 p.m. They need to insert at least 30 forints in the parking meter, and the longest possible period covered by a ticket is 3 hours. The meter takes 10, 20, 50 and 100-forint coins. During the coins being inserted, the meter continually displays the end of the parking time covered by the money inserted. The end of the parking time must not extend further than 6:00 p.m. (that is, at 17:15 p.m. the meter does not accept a 100-forint coin any more.) $a$) In what time interval is it impossible to obtain a valid parking ticket from the meter? $b$) A customer is standing in front of the meter at 11:28 a.m. He would like to stay till 7 p.m. How many times should he throw money in the meter, when, and how much if he wants to minimise the number of visits to the meter but does not want to park (not even for a single minute) without a valid ticket?