Question 6
There are $n$ students around a round table. Each has some candies, and the total number of candies is divisible by $n$. The following transfer is allowed: if a student has more candies than the student immediately to their right, one candy is transferred from the former to the latter.
Prove that, by a suitable finite sequence of such transfers, all students can be made to have equal numbers of candies.
Editorial clarification: “one candy” is explicit in the source's solution equations but accidentally omitted from its statement.
Prove that, by a suitable finite sequence of such transfers, all students can be made to have equal numbers of candies.
Editorial clarification: “one candy” is explicit in the source's solution equations but accidentally omitted from its statement.