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

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Last edited by greg1313; December 9th, 2017 at 05:59 PM.

 December 9th, 2017, 05:10 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,739 Thanks: 609 Math Focus: Yet to find out. You might have better luck getting some help if you post the question in full!
 December 9th, 2017, 05:23 PM #3 Member   Joined: Apr 2012 Posts: 72 Thanks: 3 What do you mean?
December 9th, 2017, 05:36 PM   #4
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Quote:
 Originally Posted by mathLover What do you mean?
You haven't posted a clear question. Can you explain what you mean by "find number by minimum guess"?

 December 9th, 2017, 05:44 PM #5 Member   Joined: Apr 2012 Posts: 72 Thanks: 3 Sorry, I meant find a positive integer number by minimum guesses Last edited by mathLover; December 9th, 2017 at 05:48 PM.
 December 9th, 2017, 06:01 PM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond The image displaying mechanism here seems sketchy... but there it is... Thanks from Joppy
 December 9th, 2017, 06:31 PM #7 Senior Member   Joined: Sep 2016 From: USA Posts: 520 Thanks: 293 Math Focus: Dynamical systems, analytic function theory, numerics 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
December 9th, 2017, 06:53 PM   #8
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Quote:
 Originally Posted by greg1313 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:

Last edited by mathLover; December 9th, 2017 at 06:58 PM.

December 9th, 2017, 07:06 PM   #9
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Quote:
 Originally Posted by SDK 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.

Last edited by mathLover; December 9th, 2017 at 07:11 PM.

December 9th, 2017, 08:22 PM   #10
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Quote:
 Originally Posted by mathLover 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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