MathDB

Given an ordered

n

-tuple

A=(a_1,a_2,\cdots ,a_n)

of real numbers, where

n\ge 2

, we define

b_k=\max{a_1,\ldots a_k}

for each k. We define

B=(b_1,b_2,\cdots ,b_n)

to be the “innovated tuple” of

A

. The number of distinct elements in

B

is called the “innovated degree” of

A

. Consider all permutations of

1,2,\ldots ,n

as an ordered

n

-tuple. Find the arithmetic mean of the first term of the permutations whose innovated degrees are all equal to

2

Problem Statement