Question

a certain game uses play money that comes in $7 bills and $9 bills. the banker can give $23 by handing over two $7s and one $9. But the banker cant make $22 with any combination of $7's and $9's. What is the largest sum that the banker can't make??

Answer 1

infinity ?

Answer 2

so we don't have any given amount for how many 7 dollar bills we have and how many 9 dollar bills we have?

Answer 3

don't we need that info?
i don't see how we can do the problem without that info

Answer 4

i got an answer finally

Answer 5

it is 47

Answer 6

in fact it is very easy to find, but i am not exactly sure why

Answer 7

how did you find it

Answer 8

hhhmmm. I thought it was $42 - but you can do that with $7 bills.

Answer 9

it actually has a name! given relatively prime natural numbers
\[a_1,a_2,...,a_n\] the smallest that cannot made is called the "frobenius number" and for two numbers
\[a_1,a_2\] it is
\[a_1a_2-a_1-a_2\]

Answer 10

so the answer is 47 and the proof of this formula is old and does not seem trivial

Answer 11

where do you dig up this stuff satellite :)

Answer 12

where do you think? certainly not my brain!

Answer 13

so is the proof is easy to understand?

Answer 14

but here they wanted the largest sum that cannot be made ?

Answer 15

http://en.wikipedia.org/wiki/Coin_problem

Answer 16

oh damn! hold on maybe i messed up

Answer 17

no no it is right. i just said it wrong. not the "smallest" that is stupid. the smallest is 1

Answer 18

the largest number that cannot be made is the frobeneus number and it seems that for n > 2 there is no known formula

Answer 19

third interesting problem of the night

Answer 20

I'm reading that wikipedia page - the mcnuggets number is getting me hungry

Answer 21

@emily if you ever come back i would love to know where this problem came from

Answer 22

my mind doesn't work anymore

Answer 23

you have to get up in 4 hours to teach calc at dawn anyway. get some rest

Answer 24

4 hours?

Answer 25

its 10:00 now

Answer 26

7 hours

Answer 27

but you can teach calc in your sleep, right ?
:)

Answer 28

yes
cal is super is easy to teach
i'm teaching substitution tomorrow

Answer 29

easy substitution so it will fun

Answer 30

you should get a substitute to teach it

Answer 31

that makes sense lol

Answer 32

real life applications of calculus ?

Answer 33

you know i used to bring my book with me when i taught
but i don't anymore

Answer 34

after tomorrow
\[\lim_{satellite \rightarrow \text{openstudy}}\text{time}=0\]

Answer 35

what's the highest level on openstudy satellite can't make ?