On the one hand, playing like that can give you insight. On the other hand, it can make you lose lots of time chasing an almost solution. Are you sure that arrangement of 6 was really a solution and did not require some minute bending or deformation?
"re you sure that arrangement of 6 was really a solution and did not require some minute bending or deformation?"
It's a good question, but then, it is also a perfect example of why playing around with the real object is sometimes better than applying a theoretical analysis. The question was about cigarettes, and cigarettes do bend / deform. That means that any analysis will need to take this characteristic into account. The problem is, we don't necessarily know all of the factors that need to be modelled to do a correct analysis, which is why empirical testing is still an important technique for problem solving.
Absolutely - which is why I say they need each other. They need to be merged intelligently, and purists of either camp should be taken with a grain of salt.
For infinitely long cigarettes, it is at most 24: http://library.msri.org/books/Book52/files/07bezd.pdf
Is eight attainable? http://portal.acm.org/citation.cfm?id=1450373