MathDB

Let

a_1,a_2,\ldots, a_{2013}

be a permutation of the numbers from

1

2013

. Let

A_n = \frac{a_1 + a_2 + \cdots + a_n} {n}

for

n = 1,2,\ldots, 2013

. If the smallest possible difference between the largest and smallest values of

A_1,A_2,\ldots, A_{2013}

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers, find

m+n

.
Ray Li

Problem Statement