MathDB

Let

f

be a function on

(1,\ldots,n)

that generates a permutation of

(1,\ldots,n)

. We call a fixed point of

f

any element in the original permutation such that the element's position is not changed when the permutation is applied. Given that

n

is a multiple of

4

g

is a permutation whose fixed points are

\left(1,\ldots,\frac n2\right)

, and

h

is a permutation whose fixed points consist of every element in an even-numbered position. What is the expected number of fixed points in

h(g(1,2,\ldots,104))

Problem Statement