Vrijeme: 23:12

Problemi i kavezi | Problems and Cages #1

Mentorima MNM-a je dosta zločestih matematičkih problema i zato su ih odlučili strpati u kaveze. Prva na redu je algebra! Za probleme iz algebre imaju 30 kaveza i nakon što su strpali sve probleme u kavez primijetili su da postoji barem jedan kavez s barem 34 problema u njemu i da ne postoji konfiguracija u kojoj se to ne dogodi.. Osim toga shvatili su da ako bi imali samo jedan problem manje mogli su napraviti raspored tako da nijedan kavez nema više od 33 problema. Koliko su problema iz algebre mentori smjestili u kavez?
MNM tutors have had enough of those bad-behaving math problems. That is why they decided to put every one of them into a cage. First up is algebra! For the algebra problems, MNM tutors have 30 cages and after they have put all of the problems in the cages they realized that there exists at least one cage with at least 34 problems and no matter how they rearranged the problems between the cages this scenario would always happen. Furthermore, had they had one problem less, MNM tutors would have been able to make an arrangment in which each cage has at most 33 problems inside of them. How many algebra problems are there?