MathDB

For each permutation

a_1, a_2, a_3, \ldots,a_{10}

of the integers

1,2,3,\ldots,10,

form the sum |a_1 \minus{} a_2| \plus{} |a_3 \minus{} a_4| \plus{} |a_5 \minus{} a_6| \plus{} |a_7 \minus{} a_8| \plus{} |a_9 \minus{} a_{10}|. The average value of all such sums can be written in the form

p/q,

where

p

and

q

are relatively prime positive integers. Find p \plus{} q.

Problem Statement