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Topic: 25 Attempts to Pass an Unknown Test (Read 1446 times) |
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Barukh
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25 Attempts to Pass an Unknown Test
« on: Nov 15th, 2011, 11:53am » |
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You are going to take a test consisting of 30 yes/no questions on a subject you have zero knowledge. To pass the test, you need to get all the answers right in a single attempt.
At every attempt, you supply your answers to every question, and the only information you get back is the number of questions answered correctly.
What are the chances you pass the test after 25 attempts?
I don't know the answer to this problem, but it looks quite interesting and belonging to at least Medium. I apologize if this is an old problem - haven't been around for a long time 
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: 25 Attempts to Pass an Unknown Test
« Reply #1 on: Nov 15th, 2011, 12:18pm » |
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It does sounds somewhat familiar, but if it's been posted before it would be a long while ago and I wouldn't know how to look for it.
Welcome back.
There's at least a 1 in 64 chance, since you can guarantee 24 correct answers. But you should be able to do much, much better.
I expect you should be able to get all combinations were 9 answers or less are "yes", or 21 or more; which gives you at least a 1 in 23 probability (not accounting your chances on the other cases).
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| « Last Edit: Nov 15th, 2011, 12:24pm by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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Grimbal
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Re: 25 Attempts to Pass an Unknown Test
« Reply #2 on: Nov 16th, 2011, 7:02am » |
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It is kind of a variation of mastermind, isn't it?
Is it allowed not to answer a question?
If not, all possible submissions are equivalent for the first attempt and you can as well start with an all-yes attempt.
If you have a method that starts with some yes and some no, you can convert it to a method starting with all-yes by just reversing your guess in all attempts for all the questions you initially answered by no.
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| « Last Edit: Nov 16th, 2011, 7:11am by Grimbal » |
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ThudnBlunder
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Re: 25 Attempts to Pass an Unknown Test
« Reply #3 on: Nov 16th, 2011, 9:12am » |
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on Nov 15th, 2011, 12:18pm, towr wrote:It does sounds somewhat familiar, but if it's been posted before it would be a long while ago and I wouldn't know how to look for it.
Welcome back. |
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Merely a fleeting visit, I suspect.
Not very long ago.
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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Barukh
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Re: 25 Attempts to Pass an Unknown Test
« Reply #4 on: Nov 18th, 2011, 1:11am » |
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on Nov 16th, 2011, 9:12am, ThudnBlunder wrote:
Merely a fleeting visit, I suspect. |
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Not so fast - see my attempt to revive this thread 
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Ah, I suspected Leo is somehow involved, and now I know there is an elegant solution for 25 attempts version!
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