King of Gajjumal

Phoolchand Tripathi (a.k.a Munna) is a student of Gajjumal College and wants to rule the college. Munna, being in his final year will have to leave the college if he passes the next exam, but his friend Compounder tells him that he has a way of finding whether he will fail or not. Compounder randomly gives a number $N$ and Munna has to select a number less than or equal to $N$. If the number has