Need a mathematician !

[purpleknif]

So I'm just about done with a six piece burr puzzle and as I'm test fitting things I got to wondering "how many possible combinations are there with six pieces?"
I got as far as 64 with two pieces but then you start getting into different combinations and I gave up. Anyone have an answer?

Tanx.

 

[prof65]

A possible answer is 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720, but there are some other possibilities.
E.g., if the pieces are placed on a round board or table (so there isn't a precise starting position), the answer is 6! / 6 = 120.
We need more details about your puzzle.

Roberto

 

[prof65]

Lots of info here, if you are brave

en.wikipedia.org/wiki/Permutation

 

[basement_guy]

http://www.research.ibm.com/BurrPuzzles/index.html

On this link you can find a lot info.
There is also a posibility to calculate your own puzzle.

Have fun.

 

[Philjoe5]

Maybe you should advertise for a combinatorialist.

This, from prof65'sWikipedia link:

"A mathematician who studies combinatorics is called a combinatorialist."

I learn something new every day it seems BUT unfortunately not enough to solve your puzzle

Cheers,
Phil

 

[purpleknif]

A possible answer is 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720, but there are some other possibilities.
E.g., if the pieces are placed on a round board or table (so there isn't a precise starting position), the answer is 6! / 6 = 120.
We need more details about your puzzle.

Roberto

720 doesn't seem like enough when you consider all the possibilities. My wife has a PhD in abstract mathematics and she figures 196,000 combinations. Now that I look at it as she explained it to me I think she might be right. You need to consider all the possible ways it can assemble. Parallel, cross ways,etc. I think now she might be right. She said she was gonna ask a colleague to look to be sure.
Thanks for all the replies.

 

[prof65]

When I read "how many possible combinations with six pieces" I immediately recalled my statistical studies and posted a reply without worrying about what a "burr puzzle" is (my fault). :hDe:

720 is just the number of possibile different "anagrams" (like Wikipedia calls them) that we can build with 6 different pieces, assuming that the only variable is the order of the pieces itself; but if other variables come into the game (e.g. every piece can rotate 0/90/180/270 degrees) the number of different "anagrams" grows rapidly, so your's wife's answer is probably correct (mine surely isn't).

Roberto

 

[Maryak]

I'm not sure but I think you should be looking at permutations rather than combinations? MSEXCEL has formulas for both.

Best Regards
Bob

 

[ChooChooMike]

Yo Marv !! Your services are being requested

 

[lemelman]

Take a look at this site...
http://www.research.ibm.com/BurrPuzzles/