Marinada '24

[lang=hr] Fran jako voli novce tako da i u snu razmišlja o farmama mahuna. Ove noći je sanjao o farmi mahuna u obliku beskonačne mreže. Na svakom polju je posađena jedna od $n$ različitih vrsta mahuna. Da bi ta farma ostala u skladu sa zakonima Vrbana III., za svaki pravokutnik $2 \times 3$ (ili $3 \times 2$) mora vrijediti da su sve mahune unutar njega različitih vrsta. Osim što je Fran dobar agronom, on je i golem zaljubljenik u matematiku tako da čim se ujutro probudio, počeo je razmišljati o tome koliko najmanji $n$ može biti da bi ta farma funkcionirala (bez da završi u zatvoru). Fran je riješio taj zadatak, možete li i Vi? [/lang] [lang=en] Fran loves money so much that he even dreams about bean farms. Last night, he dreamt of a bean farm shaped like an infinite grid. In each field, one of $n$ different types of beans is planted. To comply with the laws of Vrbani III, for every $2 \times 3$ (or $3 \times 2$) rectangle, all the beans within it must be of different types. Besides being a great agronomist, Fran is also a huge math enthusiast, so as soon as he woke up, he started thinking about the smallest value of $n$ that would make the farm work (without him ending up in jail). Fran solved this problem—can you? [/lang]