MathDB

For a permutation

\pi

of the integers from 1 to 10, define

S(\pi) = \sum_{i=1}^{9} (\pi(i) - \pi(i+1))\cdot (4 + \pi(i) + \pi(i+1)),

where

\pi (i)

denotes the

i

th element of the permutation. Suppose that

M

is the maximum possible value of

S(\pi)

over all permutations

\pi

of the integers from 1 to 10. Determine the number of permutations

\pi

for which

S(\pi) = M

.
Ray Li

Problem Statement