Hosted by The Math Forum## Problem of the Week 1071## Pack Them In
As a Valentine's Day present, Alice got Bob a set of infinitely many cubes, having side-lengths 1, 1/2, 1/3, ..., one cube of each side. But how to gift-wrap them? Alice knows that the harmonic series diverges, so she cannot stack one on top of another in finite space. But she also knows that the total volume of the cubes is finite, since
1 + 1/2 So the total volume is less than 1.5 and it seems as if she could just pack them all into a gift-box of dimensions 1 × 1 × 3/2. At this point she realized that a better idea would be to give Bob the cubes and the gift box and make him do the packing. Show how to arrange the cubes so that they fit into a 1 × 1 × 3/2 box. © Copyright 2007 Stan Wagon. Reproduced with permission. |

[**Privacy Policy**]
[**Terms of Use**]

Home || The Math Library || Quick Reference || Search || Help

http://mathforum.org/

The Math Forum is a research and educational enterprise of the Drexel University School of Education.

7 February 2007