A Tetrahedron

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.

Source: Based upon the 9/16/96 problem at the SMSU Problem Corner.

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