3

Part of 2023 Swedish Mathematical Competition

Problems(1)

average no of local minima in a series of real numbers in a row

Source: 2023 Swedish Mathematical Competition p3

n

be a positive integer and let

a_1

a_2

a_n

be different real numbers, placed one after the other in any order. We say we have a local minimum in one of the numbers if this is less than both of their neighbors. Which is the average number of local minima over all possible ways of ordering the numbers each other?

algebrainequalities