MathDB

Given a finite sequence of real numbers

a_1,a_2,\dots ,a_n

(

\ast

), we call a segment

a_k,\dots ,a_{k+l-1}

of the sequence (

\ast

) a “long”(Chinese dragon) and

a_k

“head” of the “long” if the arithmetic mean of

a_k,\dots ,a_{k+l-1}

is greater than

1988

. (especially if a single item

a_m>1988

, we still regard

a_m

as a “long”). Suppose that there is at least one “long” among the sequence (

\ast

), show that the arithmetic mean of all those items of sequence (

\ast

) that could be “head” of a certain “long” individually is greater than

1988

Problem Statement