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."

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.

:confused:

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?

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.

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...

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.

wouldn't the first one be 7x6x5x4x3=2520? :dunno: 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