Question: There is a spinner, divided into n unequal sectors, each labeled with the numbers 1 through n. For all integer values of k with 1

There is a spinner, divided into n unequal sectors, each labeled with the numbers 1 through n. For all integer values of k with 1 k n, the spinner lands on the number k with a probability that is exactly k2 times the probability that it lands on the number 1. Also, it turns out that there exists some number m such that the probability of the spinner landing on a number less than m is exactly 1/11 . What is the smallest possible value of n?

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