I'm not experienced in maths, so please pardon my mathematical presentation of the issue.
If n represents the number of books in a library, and x represents the number of pages in each book; what is the probability for the following event to happen:
A-E = B-D = 0
Where:
A = 1 + 2 + 3 + ... + n
B = x1 + x2 + x3 + ... + xn
C = (1+x1) + (2+x2) + (3+x3) + … + (n+xn)
D = ∑ (i+xi) " The sum of even numbers calculated in C "
E = ∑ (j+xj) " The sum of odd numbers calculated in C "
Conditions:
x (elements of B) are randomly selected from a finite set of positive integers
x > 2
u represents the number of even numbers calculated in C
w represents the number of odd numbers calculated in C
u = w = n/2 (if n = 114 then we should have 57 even numbers and 57 odd numbers in C)
n > 19
n & u & w are multiples of 19