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 Multiple ways (spoiler) by Steve Herman)

Having every side a triangle does not guarantee a tetrahedron can be formed.  The two smallest triangles may have a distance between opposing points that is smaller than the longest side.

I've checked your solutions on geometer's sketchpad and only the first does not work:
Putting a 2-3-4 next to a 4-5-6 would require a span of at least 7 while the furthest separation is about 6.72
In other words, the 7 does not fit.

Your second solution has a separation of 7.92 and the last two both have 8.82 so they all appear to be fine.

Edited on January 30, 2014, 11:10 am

Posted by Jer on 2014-01-30 11:03:28