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Topic: Problem of the Week
Replies: 0

 Problem of the Week Posts: 292 Registered: 12/3/04
Problem of the Week
Posted: Aug 16, 1993 9:53 AM

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;
description of your method as necessary/possible
to pow@forum.swarthmore.edu. 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
pow@forum.swarthmore.edu by Friday.