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Problem Of The Week #454 February 8th 2021

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,894
Here is this week's POTW:

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The numbers $x_1,\,x_2,\,\cdots,\,x_{1991}$ satisfy the equation $|x_1-x_2|+|x_2-x_3|+\cdots+|x_{1990}-x_{1991}|=1991$.

What is the greatest possible value of the expression $|y_1-y_2|+|y_2-y_3|+\cdots+|y_{1990}-y_{1991}|$, where $y_k=\dfrac{1}{k}(x_1+x_2+\cdots+x_k)$?

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Remember to read the POTW submission guidelines to find out how to submit your answers!
 
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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,894
As usual, I will give the community another week's time to attempt at last week's POTW. And I am looking forward to receiving submissions from the members!
 
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