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What is the chance that a wooden stick of size 1 meter drops on the floor in three peices and you can make a triangle with the three pieces. The chance where the stick breaks is everywhere equal.

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  • $\begingroup$ Is it guaranteed to break up into exactly three pieces? (Also, please do not put random tags.) $\endgroup$ – Deusovi Apr 24 '16 at 17:02
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0: the only way for it to happen is for the two breaks to be perfect, and the probability of hitting a single point in an interval is 0.

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  • $\begingroup$ @Deusowski That would be correct if I didn´t chance my question! $\endgroup$ – Deschele Schilder Apr 24 '16 at 17:18
  • $\begingroup$ @descheleschilder: Then it's a duplicate of puzzling.stackexchange.com/q/2110/11876 $\endgroup$ – Deusovi Apr 24 '16 at 17:21
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    $\begingroup$ Agreed, it's a duplicate. I was about to reconstruct my own answer before I realise... $\endgroup$ – Tim Couwelier Apr 24 '16 at 17:48
  • $\begingroup$ I see now that´s a duplicate too. One nice solution involves 4 equilateral triangles. 2 Triangles are next to each other, in between one, and on top, together forming a triangle. Now if my stick is the line from the top perpendicular to the bottom, length 1, than one part of my stick has to be smaller or equal than 1/2, because the other 2 pieces add up to 1/2 or more. So for this stick, one breaking point has to be in the central triangle. The same is true for the other two sticks, so the breaking points have to be in the central triangle, wich is 25 percent of the total area of triangles. $\endgroup$ – Deschele Schilder Apr 26 '16 at 17:44

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