Need a mathematician !

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purpleknif

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

Best Regards
Bob
 
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