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.

(In reply to re(2): Multiple ways (spoiler) by Steve Herman)

Do you need to check all spans, or only the longest?

I'm pretty sure you only need to check the longest. 

To check whether 7 spans I put together the triangles that don't involve 7.  These are the smaller triangles.  To check whether 6 spans I'd put together the triangles that don't involve 6.  But one or two of these will involve 7 and be larger triangles. 

This might be a good perplexus problem in its own right...

Posted by Jer on 2014-01-30 15:54:33