We're baaack! After a two week recovery period, Problem of the Week returns...
The problem of the week is a regular instalment here at the geometry forum. Each weekend a high-school level geometry problem will be posted (though levels may be different in the summer), and the following weekend a summary of solutions will be posted.
Please do not post solutions to the problem of the week; instead mail you answer along with as detailed a description of your method as necessary/possible to email@example.com. Solutions should be received by midnight Friday so they can be combined and posted over the weekend.
Problem of the Week 8/16 - 8/20 1993
You are given 27 rectangular solids of dimensions a,b,c. How can they be packed to fit into a cube whose sides are a + b + c? (One should add that a, b, and c are not too different. If c/a and c/b were extremely large, for instance, it would be trivial to stack them like logs. A precise statement would be something like (a+b+c)^3 - 27abc < abc.)
Again, DO NOT POST SOLUTIONS. Mail them to firstname.lastname@example.org by Friday.