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 Replies: 8 / Views: 1,952 |
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Pillar of the Community
United States
535 Posts |
I posted these on another forum, so if you've seen them, please don't answer.
Here are a few "riddles" that I've thought through.
1) Every day I go the cafe at work and buy a coffee for a $1 (tax included). The lady will give me back whatever change I want. If I pay with a $100 I can ask for change in any combination of $50, $20, $10, $5, $2, or $1's.
My goal is to see the most number of bills (so I can try to find a binary repeater radar error star note)
I start out with a $100 and put the change each day in my desk. I only use that money in my desk for coffee each day. If I start out with a $100 bill how should I ask for change each day so that I can search through the most number of bills?
2) When you go to the bank and get a brand new strap of $1 bills, what are the odds that the strap you get will have a bill that ends in three identical numbers (e.g. 12345666)? (Assuming there are no star notes in the strap)
I was fascinated when I figured out the anwer to each of these. Try to figure out the answers before you read the other responses.
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Pillar of the Community
United States
1031 Posts |
1) The highest possible: 1-$50, 2-$20's, 1-$5, 2-$2's?
2) Odds: 1 in 2?
Edited by docsfishn
11/20/2008 01:54 am
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Rest in Peace
United States
2668 Posts |
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Pillar of the Community
Poland
3201 Posts |
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Pillar of the Community
United States
891 Posts |
It shouldn't matter what you ask in for in change it should be the same amount of notes regardless. You would be able to see 100 notes no matter the combination. Unless I am missing something.
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Pillar of the Community
Australia
2830 Posts |
if I understand the riddle correctly - and I'm not certain that I do:
$99 in change could be 1 x$50, 2 x $20, 1 x $5, and 2 x $2: total six notes.
But if you asked for 99 x $1, then you'd have 99 notes to examine.
Trying maximize the number of notes over a week, I think you'd still end up with an answer of 99, because time you go back, your change is $1 less than whichever note you tender.
second riddle: how many notes in a strap ?
Peter
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Pillar of the Community
United States
632 Posts |
I guess if you looked at the 100 you started with, and got all ones, you would have searched 100 notes.
to get a bill ending in a 3 digit combination, I think its 111 notes between, say, the bill ending in 333 and the next note of 444. Right?. If there are 100 notes in a strap, you should get one note every 2 straps, or 1 every 111 notes. Man!. you know how I feel about math!.
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Pillar of the Community
 United States
535 Posts |
1) The goal here is to look through the most different bills over the course of 100 days while you spend $1 a day on coffee. So when pay with $100 bill you decide how you get your change: for example you could get 99 $1 bills or you could get 1$50, 2-$20, 1-$5, 2-$2. Then the next day pay with a $2 and get a $1 in change.
I would think that there would be some way to decide how you get your change back so that you could maximize the number of bills you see. It turns out that it doesn't matter how you get your change, over the course of 100 days, you will always see 100 bills.
2) There are 100 notes in a brand new strap. The notes are consecutivly numbered for example: 12312101-12312200. So it seems that every strap should have one note that ends in three identical digits. So if the first bill in your strap is 12312401 then in that strap will be 12312444. if the first bill in your strap is 12312501 then in that strap you will have 12312555.
I would have thought that every strap I get (1005) would have a bill that ends in a triple digit. As it turns out there is only a 90% chance that the strap you get will have bill that ends in a triple digit.
If you have 10 straps that are sequential (e.g. the first bill in each strap is 12312001, 12312101, 12312201, 12312301, 12312401, 12312501, 12312601, 12312701, 12312801, 12312901) 8 of the straps have 1 bill that ends in triple digits, the first strap does not have any, but the last strap has 2 - 12312999 and 12313000. So your odds of getting a strap that ends in a triple digit is only 90%.
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Pillar of the Community
United States
632 Posts |
WOOHoo!. I hope you don't mind if I declare myself the winner. I got the total number of notes searched and 111 notes IS 90%.
...and I still hate math.
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Replies: 8 / Views: 1,952 |
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Posted 11/20/2008 2:17 pm
