MathDB

Let

n

be a positive integer. Let us call a sequence

a_1,a_2,\dots,a_n

interesting if for any

i=1,2,\dots,n

either

a_i=i

a_i=i+1

. Let us call an interesting sequence even if the sum of its members is even, and odd otherwise. Alice has multiplied all numbers in each odd interesting sequence and has written the result in her notebook. Bob, in his notebook, has done the same for each even interesting sequence. In which notebook is the sum of the numbers greater than by how much? (The answer may depend on

n

Problem Statement