December 9th, 2017, 03:49 PM  #1 
Member Joined: Apr 2012 Posts: 72 Thanks: 3  find number by minimum guess Thanks! Last edited by greg1313; December 9th, 2017 at 04:59 PM. 
December 9th, 2017, 04:10 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,634 Thanks: 567 Math Focus: Yet to find out. 
You might have better luck getting some help if you post the question in full!

December 9th, 2017, 04:23 PM  #3 
Member Joined: Apr 2012 Posts: 72 Thanks: 3 
What do you mean?

December 9th, 2017, 04:36 PM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,634 Thanks: 567 Math Focus: Yet to find out.  
December 9th, 2017, 04:44 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 04:48 PM. 
December 9th, 2017, 05:01 PM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,852 Thanks: 1077 Math Focus: Elementary mathematics and beyond 
The image displaying mechanism here seems sketchy... but there it is...

December 9th, 2017, 05:31 PM  #7 
Senior Member Joined: Sep 2016 From: USA Posts: 435 Thanks: 247 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, 05:53 PM  #8  
Member Joined: Apr 2012 Posts: 72 Thanks: 3  Quote:
Last edited by mathLover; December 9th, 2017 at 05:58 PM.  
December 9th, 2017, 06:06 PM  #9  
Member Joined: Apr 2012 Posts: 72 Thanks: 3  Quote:
Last edited by mathLover; December 9th, 2017 at 06:11 PM.  
December 9th, 2017, 07:22 PM  #10  
Senior Member Joined: Sep 2016 From: USA Posts: 435 Thanks: 247 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
Suppose WLOG that there are $2^n$ numbers and you ask whether it is larger or smaller than $2^{n1}$ and he says smaller. Your next question is going to be "Is it larger or smaller than $2^{n2}$? 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 $2^{n1} + 2^{n2}$ 4. Lied on last step, larger than $2^{n1} + 2^{n2}$.  

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