perplexus.info :: Numbers : Alternating Differences

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?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required mean value of this sum taken over all possible permutations(n+1)(n-2)/3.
For an explanation, refer to the solution submitted by Larry in this location.

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

Subject	Author	Date
No Subject	K Sengupta	2023-12-16 08:12:32
No Subject	Hedda Dunn	2023-12-16 07:28:54
No Subject	Larry	2023-12-07 09:21:32

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