[QUOTE=xilman]Not quite the same as the classical solution, as Paul's puts thes ticking-out ends of the matches in contact too. However, it's the same basic idea.[/QUOTE]

Not so sure. I think that's exactly the classic solution, apart from the fact that the classic one could rest on a table-top, so the vertical one doesn't extend downwards.

If the sticking-out ends don't touch, then that pair of matches doesn't touch, surely?

[QUOTE=fatphil]Not so sure. I think that's exactly the classic solution, apart from the fact that the classic one could rest on a table-top, so the vertical one doesn't extend downwards.

If the sticking-out ends don't touch, then that pair of matches doesn't touch, surely?[/QUOTE]Perhaps you're right.

I'm starting to get parity errors as my memory gets older.


Paul

[QUOTE=xilman]I'm starting to get parity errors as my memory gets older.
[/QUOTE]

It could be worse, you could be a socialite who has party errors. Or an economist with Pareto errors. Or an industrial chemist with purity errors!
Or...

[QUOTE=xilman] Lay three cylinders flat on a surface such that their axes are at 120 degrees to each other and the ends touching.[/QUOTE]

For the purpose of description, let's place the origin of a coordinate system at the center of your arrangement and align the z-axis to be perpendicular to the "surface". Now, we can futher specify that one of the cylinders has its axis parallel to the x-axis. One end is near the origin, and the other is a match length away in the +x direction.

Question: Does the axis of each cylinder (extended) pass through the origin?

As I understand your "classical" arrangement, the second layer is located in a plane where z = +1 diameter.
Further, one of those matches extends in the -x direction.

Question: Where does the +x match touch the -x match?
It appears to me that there is a gap.

[QUOTE=fatphil]It could be worse, you could be a socialite who has party errors. Or an economist with Pareto errors. Or an industrial chemist with purity errors!
Or...[/QUOTE]

A writer with parody errors

[QUOTE=Wacky][SPOILER]
Further, one of those matches extends in the -x direction.
[/SPOILER][/QUOTE]

is incorrect.

[QUOTE=fatphil]is incorrect.[/QUOTE]

But
[QUOTE=xilman] such that the six cylinders are at 60 degree spacings.[/QUOTE]

As a understand it, the only way to have 6 cylinders spaced at 60 degree intervals will require them to be in pairs where those two are 180 degrees apart.

Note:
I am not describing the solution (see PZ's diagram), but rather the arrangement described by PL (xilman).

There is also a second objection to this solution (Xilman’s, although I note that he does not claim it as his). The incircle of an equilateral triangle has of necessity diameter < the length of its sides. The length of its sides is the diameter of the match that is supposed to pass through this circle. Surely this is a contradiction that means that Xillman’s vertical match (the one on Wacky’s z-axis) can not be put in place as suggested.

The diagram here should make this quite clear.
[url]http://mathworld.wolfram.com/Incircle.html[/url]

Off topic: (or is it?)

I just checked for new posts and received this reply --

[QUOTE]vBulletin Message
Sorry - no matches.[/QUOTE]


:)

akruppa,

There is a better solution with matches that have square-cross section, as you assume.

Without loss of generality, we may assume the matches are actually cubes. (Really SHORT matches!) Then, in fact we can make 8 of them touch! Just stack them into one cube made up of 8 smaller cubes. They all touch at the corner in the center of the big cube.

Now, if you want them to touch along at least a 1-dimensional slice, that's a different story. But since, in the real world, *touching* is really interactions with the weak force...I think my solution is fine. :D

Hehe I wondered when someone would think of that.
Some riddles have very odd solutions that still work if you're change your assumptions. A cube may always have 6 sides, 8 corners, and 12 edges, but that doesn't mean all things called "cubes" are in fact actual cubes.
[spoiler] Ice cubes, or puns on cues, etc. [/spoiler]
Rectangles may in fact usually include squares. This may be annoying to people like me who were brought up thinking that rectangles may not have equal sides, but it's still a fact that technically, squares can also be considered rectangles. To be more accurate, I'd use the word quadrilateral.