IMC2015, problem 8
Source: IMC2015
July 30, 2015
college contestscombinatoricsIMC2015
Problem Statement
Consider all words of length 26 in the Latin
alphabet. Define the \emph{weight} of a word as , where
is the number of letters not used in this word. Prove that the sum
of the weights of all words is .Proposed by Fedor Petrov, St. Petersburg State University