Question

Kevin has a sequence of integers a1, a2, ..., an. Define the strength of the sequence to be |a1 - a2| + |a2 - a3| + ... + |an-1 - an| + |an - a1|. Kevin wants to make his sequence stronger, so he reorders his sequence into a new sequence b1, b2, ..., bn. He wants this new sequence to be as strong as possible. What is the largest possible strength of the resulting sequence?

Answer 1

a5=31a5=31;


a4=31−5=26a4=31−5=26;



a3=26−5=21a3=26−5=21;



a2=21−5=16a2=21−5=16;


a1=16−5=1a1=16−5=1.


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Answer 2

a5=31a5=31;


a4=31−5=26a4=31−5=26;



a3=26−5=21a3=26−5=21;



a2=21−5=16a2=21−5=16;


a1=16−5=1a1=16−5=1.