(In reply to Probable solution
This is what I found also: 3*sqrt(2)/4.
The way I arrived at the same placement that produced this, was to imagine a box shaped like a cube. Then remove the top square to leave an open box, and see what way to fit the square into the box with the most wiggle room. This would be vertically along a diagonal of the base, but could be tilted and allowed to grow. It would have to stop growing when it reached the point where it hit the top and sides simultaneously at two corners and the bottom and sides simultaneously at the other two corners. This situation leads to the equations that you give and solve.
Posted by Charlie
on 2004-12-26 19:01:10