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        riddles >> hard >> Filling the Box
        
(Message started by: Sebastian Craine on Aug 22^nd, 2005, 2:41pm)

Title: Filling the Box
Post by Sebastian Craine on Aug 22^nd, 2005, 2:41pm

Since you spoke of a rectangular box, it is safe to assume the solid might be a cube (not that it matters). You failed to stipulate that one would need to fill the box with a finite number of incongruent cubes, as it is plausible if you would have an infinite number.

Let the box be a square with side length N. Then fill the box with incongruent cubes with side lengths that are part of an infinite sequence with sum N.

Title: Re: Filling the Box
Post by Icarus on Aug 22^nd, 2005, 5:58pm

You are mixing dimensions. Your solutions works for filling a one dimensional "box". It does not work in 2 or higher dimensions, though.

There is already a thread for this puzzle (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1061630044). You may find the discussion there illuminating.