Question 100
There are $30$ students in a mathematics competition. We wish to give them a total of $N$ candies so that the following hold:
(i) Each student gets at least one candy.
(ii) Any student with a larger score gets more candies than any student with a lower score.
(iii) Any two students with the same score get the same number of candies.
Determine the smallest possible value of $N$ for which the candies can be given in some way, no matter what the ranking of the students is.
(i) Each student gets at least one candy.
(ii) Any student with a larger score gets more candies than any student with a lower score.
(iii) Any two students with the same score get the same number of candies.
Determine the smallest possible value of $N$ for which the candies can be given in some way, no matter what the ranking of the students is.