perplexus.info :: Just Math : Optimal location

Optimal location (Posted on 2014-10-10)

Find a point that minimizes the sum of the distances to N given points on a number line.

No Solution Yet Submitted by Art M

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re: solution (spoiler) same result, diferent reasoning

Comment 2 of 2 |

(In reply to solution (spoiler) by Charlie)

Consider n=1.

Clearly the point itself constitutes the answer.

Adding two points, one to the left to the existing point,

another to the right does not affect the solution.

Add another two points...etc

So much for the odd case.

SImilar reasoning for the even case, except starting

anyplace between the two initial points.

Posted by Ady TZIDON on 2014-10-10 12:19:14

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