# Martin Gardner - "Can you make 7 cylinders all touch each other?" 50 years later...

A Tale of Touching Tubes

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.

Note by Dan Krol
7 years, 2 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

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".

- 7 years, 2 months ago

I'm interested as to why you have cigarettes in the first place... Bad habit. :D

- 7 years ago

What's a habit worse than cigarettes is not understanding a problem correctly the first time around.

- 7 years ago

Haha, I am victim to this habit. :D

- 7 years ago

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.

Staff - 7 years, 2 months ago

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.

- 7 years, 2 months ago

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...

- 7 years, 2 months ago

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."

- 7 years, 2 months ago

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".

- 6 years, 12 months ago

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.

Staff - 6 years, 11 months ago