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  #1  
Old 01-22-2006, 11:15 AM
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Abstract thinkers and mathematicians brain teasers

What are the answers to these 2 questions and how did you figure them out?

"How many different ways can five people be seated in seven chairs?"

"Using American paper currency, how many different ways can you make $63 using 6 bills? List the combinations."
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Old 01-22-2006, 11:33 AM
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I suck at this stuff but why not post a "guess"

1) 45
2) 1 way, 50 plus 5 plus 5 plus 1 plus 1 plus 1

That is my guess after 4 hours sleep and going to bed at around 3 am last night.

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Last edited by Wagner; 01-22-2006 at 12:28 PM.
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  #3  
Old 01-22-2006, 12:19 PM
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Quote:
Originally Posted by WagnerX5
I suck at this stuff but why not post a "guess"

1) 40
2) 1 way, 50 plus 5 plus 5 plus 1 plus 1 plus 1

That is my guess after 4 hours sleep and going to bed at around 3 am last night.

Thanks Wagner - BTW, I don't know the answers, I'm looking for someone who does!

So how did you come up with 40 for the first one? And I can think of another couple of combos for the second one:
20+20+20+1+1+1
10+10+20+20+1+2

any more?
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Old 01-22-2006, 12:28 PM
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wasn't aware we were using the old $2.00 bill as currency. I was using the standard: 1,5,10,20,50...although I'm not sure how I missed the 3 twenty/3 one combo doh.

For the second I changed my answer to 45, I forgot it was 7 seats and 5 people. (I was thinking of the 6 in the 2nd question).
So for that I figure 5 x 7 is 35 however there are two open seats at all times so add 2 to the seat combo and get 9 seats for a 5 times 9 = 45 solution...again...no sleep equals I may be WAY off.
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  #5  
Old 01-22-2006, 12:36 PM
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does order matter for the first one (ie, there is a seat 1-5?) or are we looking at the chairs in a circular format? (where there is no real seat 1-5, rathar just what they are next to)
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Old 01-22-2006, 02:41 PM
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Quote:
Originally Posted by Vitriol
does order matter for the first one (ie, there is a seat 1-5?) or are we looking at the chairs in a circular format? (where there is no real seat 1-5, rathar just what they are next to)
Good question - it didn't say anything about an order, but it did show a picture of 7 seats in an airplane...
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Old 01-22-2006, 02:46 PM
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For the first there are two ways to solve it... Vitriol hit it on the mark.

If I believe order matters, then it's nPr and if it doesn't matter, then nCr
I'll double check, but that should be it. Then it'll be either like 7! + 6! or something like that.
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Old 01-22-2006, 06:13 PM
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wouldn't the first one be 7x6x5x4x3=2520? the way i figure it, the first guy has 7 choices, which gives the second guy 6 choice, the third guy 5 choices, etc.

I could only think of 3 ways to make $63:

50+5+5+1+1+1
20+20+20+1+1+1
20+20+10+10+2+1
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Last edited by x5GuyInLA; 01-22-2006 at 06:38 PM.
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