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December 9th, 2017, 04:49 PM   #1
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find number by minimum guess


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File Type: jpg 1.jpg (13.9 KB, 12 views)

Last edited by greg1313; December 9th, 2017 at 05:59 PM.
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December 9th, 2017, 05:10 PM   #2
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You might have better luck getting some help if you post the question in full!
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December 9th, 2017, 05:23 PM   #3
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What do you mean?
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December 9th, 2017, 05:36 PM   #4
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Originally Posted by mathLover View Post
What do you mean?
You haven't posted a clear question. Can you explain what you mean by "find number by minimum guess"?
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December 9th, 2017, 05:44 PM   #5
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Sorry, I meant find a positive integer number by minimum guesses

Last edited by mathLover; December 9th, 2017 at 05:48 PM.
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December 9th, 2017, 06:01 PM   #6
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The image displaying mechanism here seems sketchy... but there it is...
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December 9th, 2017, 06:31 PM   #7
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The follow up question which is a power of 2 kind of gives it away. In case you still need a hint:

https://en.wikipedia.org/wiki/Binary_search_algorithm
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December 9th, 2017, 06:53 PM   #8
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Quote:
Originally Posted by greg1313 View Post
The image displaying mechanism here seems sketchy... but there it is...
I fixed the image, but I can't edit the original post. Here is the image:


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December 9th, 2017, 07:06 PM   #9
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Quote:
Originally Posted by SDK View Post
The follow up question which is a power of 2 kind of gives it away. In case you still need a hint:

https://en.wikipedia.org/wiki/Binary_search_algorithm
I thought to solve this by using binary search algorithm, but the problem is, that according to the question, who you ask him if the number is smaller than ... or greater than ... , he is allowed to lie to tyou once.

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December 9th, 2017, 08:22 PM   #10
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I thought to solve this by using binary search algorithm, but the problem is, that according to the question, who you ask him if the number is smaller than ... or greater than ... , he is allowed to lie to tyou once.
Correct, but this doesn't matter.

Suppose WLOG that there are $2^n$ numbers and you ask whether it is larger or smaller than $2^{n-1}$ and he says smaller. Your next question is going to be "Is it larger or smaller than $2^{n-2}$? If he answers larger, you wonder if he lied in the previous step. Can you think of a clever way to change the question so that you can distinguish the 4 cases?
1. Truthful last step, smaller
2. Truthful last step, larger
3. Lied on last step, smaller (than $2^{n-1} + 2^{n-2}$
4. Lied on last step, larger than $2^{n-1} + 2^{n-2}$.
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