Martin Gardner - "Can you make 7 cylinders all touch each other?" 50 years later...
Using computers to solve a system of 20 variables, a challenge to make seven cigarettes touch each other is answered. Gardner himself technically answered his own challenge, but not in such an interesting way, because the ends of the cigarettes were involved. Now it can be done with 7 infinitely long cigarettes.
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Dan Krol
7 years, 2 months ago
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2nd Try: Stand a cigarette upright. Then lay 3 flat cigarettes all touching it and each other , which is possible if they're 120 degrees apart. Do the same on top of that with another 3, but the mirror image of the first.
I'm not sure why we need to invoke "infinitely long cigarettes".
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I'm interested as to why you have cigarettes in the first place... Bad habit. :D
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What's a habit worse than cigarettes is not understanding a problem correctly the first time around.
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Haha, I am victim to this habit. :D
Interesting, I didn't consider that making the cigarette longer could make it easier. But that's because the cigarettes are of a certain thickness. Maybe the solution from the article still wouldn't work with real cigarettes. Maybe Virginia Slims, heh.
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In re-reading this question, I understand now that what was done recently by those mathematicians was to find a solution using 7 infinitely long cigarettes, which is much harder to do. Again, I had fallen back on my bad habit of solving a problem before I've fully understood it.
I was once asked the "how many" version of this question for both finite and infinite cylinders as an interview question. I'm still kind of at a loss what was expected as a "good" interview response...
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Update: I just reached out to one of the people who interviewed me at that company to let them know that the problem is now solved. He said "Worst interview question ever."
Stand a cigarette upright. Then lay 3 flat cigarettes all touching it and each other , which is possible if they're 120 degrees apart. Do the same on top of that with another 3, but the mirror image of the first. I'm not sure why we need to invoke "infinitely long cigarettes".
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An equilateral triangle made of cigarettes is going to have a much larger area than the cross section of a cigarette, so I don't see how an upright cigarette can touch all three of them. Also, if you lay them "flat" as you say, that requires cigarettes which are not infinitely long, or else the sides of the triangle will run into each other. So, the length of the cigarettes is relevant.
Maybe I'm not imagining your model correctly though.