MathDB
IMC2015, problem 8

Source: IMC2015

July 30, 2015
college contestscombinatoricsIMC2015

Problem Statement

Consider all 262626^{26} words of length 26 in the Latin alphabet. Define the \emph{weight} of a word as 1/(k+1)1/(k+1), where kk is the number of letters not used in this word. Prove that the sum of the weights of all words is 3753^{75}.
Proposed by Fedor Petrov, St. Petersburg State University