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The medians of medians (Posted on 2014-12-20) Difficulty: 4 of 5
<begin> For a triangle with integer sides a,b,c (none over 2000) evaluate the triplet of its medians ma , mb , mc .
Let those three become sides of a new triangle i.e. (a,b,c) =(ma , mb , mc ).
<end>

It is up to you to find a triplet (a,b,c) such that the above procedure can be executed a maximal number of times, creating sets of “medians“ with integer values only.

The answer should include: (a,b,c) and all interim sets of medians.

Rem: Can be solved analytically.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution | Comment 5 of 6 |
(In reply to re: Solution by Harry)

As I understood the problem, Harry. Ady was inferring the points intersected by the medians with the sides of the triangle (the medial points) would be the vertices of the inner triangle.

Edited on December 20, 2014, 6:48 pm
  Posted by Dej Mar on 2014-12-20 18:47:24

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