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A Tetrahedron (Posted on 2014-01-30) Difficulty: 2 of 5
You are given six sticks of integral lengths 1, 2, 3, 4, 5 and 6. Using these sticks, can you make a tetrahedron (4-sided, 3-D figure, with a triangle on each side)?

If so, show how. If not, replace any one of the sticks with the smallest stick of integral length greater than 6 that allows you to build such a tetrahedron and show how it can be done.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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Solution Multiple ways (spoiler) | Comment 1 of 4
No, it cannot be done.  In any triangle, every non-degraded triangle, each side must be less than the sum of the other two sides.  This is not possible with a stick of length 1, if all of the other sticks are larger integers.

It is possible if the 1-stick is replaced with a 7-stick.

One way is to form the following triangles:
7-6-2
7-5-3
6-5-4
2-3-4

The above also works if the 4 and 3 sticks are swapped.  Namely,
7-6-2
7-5-4
6-5-3
2-4-3

Also
7-6-3
7-5-4
6-5-2
4-3-2

Also
7-6-4
7-5-3
6-5-2
4-3-2

While I may have missed one, I only see 4 ways



  Posted by Steve Herman on 2014-01-30 09:52:00
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