Math Is Fun Forum
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#1 2011-08-31 15:39:56
- Nitin Agarwal
- Guest
Puzzle
The Puzzle: At a restaurant, how could you choose one out of three desserts with equal probability with the help of a coin?
Bonus: What if the coin is biased and the bias is unknown?
#2 2011-08-31 18:34:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Puzzle
Hi;
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.
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#3 2011-08-31 22:35:45
- divyas
- Member
- Registered: 2011-08-31
- Posts: 4
Re: Puzzle
Here is your solution and if you still need any questions then please feel free to ask me.But i havent done on my own,my friend solved this one.
Toss the coin twice. Let TH, HT and TT correspond to the three choices. If HH, repeat. This takes 8/3 tosses on average. If the coin were biased, TH and HT would occur with equal probabilty. So one strategy could be to assign THHT, HTTH and THTH to the three choices, with other 4-toss outcomes rejected. An alternative strategy is to assign HTT, THT and HTT to the three choices, with other 3-toss outcomes rejected.
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#4 2011-09-01 01:51:15
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Puzzle
For an unbiased coin, that method is fine.
Couldn't get anything for a biased coin yet.
Maybe we should find the bias first?
edit: Didn't read the explanation properly, I see that it explains for a biased coin too. Looks okay to me.
my friend solved this one.
Hmmm, bobbym knows your friend too!
Last edited by gAr (2011-09-01 02:11:13)
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#5 2011-09-01 02:13:32
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Puzzle
Hi gAr;
Makes you wonder on this one if that is the only idea that works?
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.
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#6 2011-09-01 02:30:51
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Puzzle
Hi bobbym,
I didn't read the explanation, but verified the strategy with an absorbing markov chain,
We may conduct the same thing for a biased coin.
Anyway, did you have a different idea?
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#7 2011-09-01 07:56:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Puzzle
Hi gAr;
Nothing that worked.
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.
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#8 2011-09-02 18:08:16
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Puzzle
Hi bobbym,
Okay.
For a biased coin also we can proceed with the same idea:
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#9 2011-09-02 18:10:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Puzzle
Hi gAr;
I will look at that. Taking a little break now.
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.
Offline
#10 2011-09-02 18:10:54
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Puzzle
Hi,
Okay, see you later...
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
Offline
#11 2011-09-02 18:53:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Puzzle
Hi gAr;
Okay I think it checks out!
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.
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#12 2011-09-02 19:30:02
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Puzzle
Hi bobbym,
Okay, thanks for looking!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
Offline
#13 2011-09-02 19:31:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Puzzle
Hi gAr;
I am putting it in my notes so it is definitely right!
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.
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