High School Can Six Pencils Be Arranged to Each Touch the Other Five?

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The discussion centers on the challenge of arranging six pencils so that each touches the other five, a three-dimensional problem derived from a Martin Gardner puzzle. Participants debate the feasibility of various solutions, noting that no solution exists if all pencils are confined to a single layer. Some argue that a non-planar arrangement could work, while others express skepticism about the accuracy of proposed solutions due to gaps that prevent full contact. The conversation also touches on the complexity of the geometry involved and the potential for alternative solutions, including the possibility of extending the problem to seven pencils. Ultimately, the consensus remains uncertain, with many seeking a more rigorous mathematical approach to validate their findings.
  • #31
gmax137 said:
The question now (nearly 3 months later) is, has @DaveE painted his bathroom yet?
Yep. Stuck on the tile though. I don't know if I should do it myself or pay someone. Apparently thinking about it harder doesn't actually work. However, it is the path of least resistance (the least usable bathroom, too). One year+ on this project, I don't think I'd make it as a remodel contractor.
 

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