perplexus.info :: Numbers : Alternating Differences

Home > Numbers

Alternating Differences (Posted on 2023-12-07)

Let X₁, X₂, X₃, ..., X_n be a permutation of the integers 1,2,3,...,n.

Consider the sum:
abs(X₁-X₃) + abs(X₂-X₄) + abs(X₃-X₅) + ... + abs(X_n-2-X_n).

What is the mean value of this sum taken over all possible permutations?

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( You must be logged in to post comments.)

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info