Matches
 

Can you arrange seven matches so that each one touches the other six?

Alex

Are we talking about wooden matches or paper matches?

With two matches, place the heads together to form a "V" of about 60 degrees. Slide a third match between them so that all three heads touch.
[SPOILER] Repeat to form a second group. Place one group on top of the other at right angles. All six will touch the other five[/SPOILER]


[SPOILER]
Bend the last match in the middle and place the two ends on the junctions of the other match heads
[/SPOILER]

[QUOTE=philmoore]Are we talking about wooden matches or paper matches?[/QUOTE]
I don't think that it matters. They each have similar properties -- length, thickness, etc.

[SPOILER] and they can be bend without causing the two parts to separate [/SPOILER]

heh... leave it to mathematicans to spot loopholes in problem! :smile:

[U]Without[/U] bending or breaking any matches!

Phil, they have square cross-section, but I don't think it matters.

Alex

[QUOTE=akruppa]heh... leave it to mathematicans to spot loopholes in problem![/QUOTE]
What mathematican? I'm an Engineer!

[QUOTE]
[U]Without[/U] bending or breaking any matches![/QUOTE]
Spoil sport :)

[QUOTE=akruppa]heh... leave it to mathematicans to spot loopholes in problem! :smile:

[U]Without[/U] bending or breaking any matches!

Phil, they have square cross-section, but I don't think it matters.

Alex[/QUOTE]
There is a classic solution with 7 mutually touching right circular cylinders. It's essentially the one which Wacky gave, assuming that I read his description correctly.


Paul

If I understand Wacky's solution, he required that one match could be bent. Can it be done without bending?

Alex

[QUOTE=akruppa]If I understand Wacky's solution, he required that one match could be bent. Can it be done without bending?

Alex[/QUOTE]I misunderstood.

To be honest, I didn't read it properly.

Here's the classical solution which uses right circular cylinders:

[spoiler]Lay three cylinders flat on a surface such that their axes are at 120 degrees to
each other and the ends touching. Note that there will be a triangular hole
at the center of the shape.

Build another such shape with three more cylinders and place it on top of
the first three such that the six cylinders are at 60 degree spacings.

Slide a seventh cylinder down the (now hexagonal) hole in the center.[/spoiler]


Paul

Correct! I found this [URL=http://www.loria.fr/~zimmerma/problems/matches.html]image[/URL] of the solution on Paul Zimmermann's page.

Alex

[QUOTE=akruppa]Correct! I found this [URL=http://www.loria.fr/~zimmerma/problems/matches.html]image[/URL] of the solution on Paul Zimmermann's page.

Alex[/QUOTE]
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.


Paul