Math Is Fun Forum

Peggy

Guest

a perplexing (at least to me) problem

I am a fan of your page and enjoy playing the games whenever I need some down time. Learned a lot from you, stuff they didn't teach us at school, or maybe it was a day I missed - there were a few.

Now, I'm posed with a question my old brain cells cannot calculate. I'm writing a story and in it is a device which uses 9 crystals. There are three each of three shapes (3-sided, 4-s'ded, 6-sided) which fit into three rows, each row containing three holes of the same shape. I've tried to figure the permutations to come up with the possible number of 'combinations' but get stuck because of the limitation with the placement, since each crystal has only three possible spots in its row. 

My brain wants to say that there are 3 rows, each with 6 possiblities which brings 27 possible configurations of crystals. But that just doesn`t seem right.

Help me Obi-Wan, you are my only hope! Thank you!!!
Peggy

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: a perplexing (at least to me) problem

Hi Peggy;

Welcome to the forum!

Are you saying that each type of crystal has only row for it?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Peggy

Guest

Re: a perplexing (at least to me) problem

Thanks for your question. Love your avatar!!!

Yes... top row = 3 sided holes/crystals
         middle = 4 sided holes/crystals
         bottom = 6 sided holes/crystals

The crystals are interchangeable within their row. Each crystal is a different color with different properties.

Thanks again!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: a perplexing (at least to me) problem

Hi Peggy;

A few more. So each 3 sided crystal is different? So is each 4 sided and 6 sided?

If they are then you have 216 ways to arrange the 9 crystals in the 3 rows.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Peggy

Guest

Re: a perplexing (at least to me) problem

Thank you for your help!  I was way off.  Yes, each crystal is different so your answer is the perfect one!!
Thank you again! I was going crazy trying to figure it out.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: a perplexing (at least to me) problem

Hi Peggy;

Your welcome, glad to help.

If your story grows into a novel do not forget to mention me as a technical adviser. Or maybe you can write me in with a small part.

When they make the movie please demand that Tom Cruise plays my character.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.