MathDB

A permutation of the integers

1901, 1902, \cdots, 2000

is a sequence

a_1, a_2, \cdots, a_{100}

in which each of those integers appears exactly once. Given such a permutation, we form the sequence of partial sums

s_1 = a_1,\;\;s_2 = a_1 + a_2,\;\;s_3 = a_1 + a_2 + a_3, \; \ldots\;, \; s_{100} = a_1 + a_2 + \cdots + a_{100}.

How many of these permutations will have no terms of the sequence

s_1, \ldots, s_{100}

divisible by three?

Problem Statement