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A thousand natives Knights, Knaves and Jokers  Weight: 5 Liked the puzzle: 100% 30.12.2009
A MegaMind was captured and brought to an island where a 1000 natives live. Some natives always tell the truth and some always lie. There is at least one truth teller on the island. The MegaMind was promised to be kept alive if he can point out the liars from the truth-tellers. Every hour, the MegaMind is allowed to call up a number of natives and ask a single question: "How many of you are truth-tellers?" or "How many of you are the liars?" How many hours does the MegaMind need before he can determine the liars/truth-tellers?
Comments:   7 check your solution  

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idler_
 
Rating: 106
Group: Moderators
2011-01-28 19:40:30
Reserved.
dddfff
 
Rating: 228
Group: Moderators
2011-02-26 01:13:44
>Every hour, the MegaMind is allowed to call up a number of natives and ask a single question: "How many of you are truth-tellers?" or "How many of you are the liars?"

To whom does the MegaMind address this question?

For example, is the MegaMind asking just one native from among those called up to give a numerical answer concerning the whole ensemble? Or everyone assembled to give their own numerical answer concerning the whole ensemble?
alan
 
Rating: 231
Group: Moderators
2011-02-26 09:54:01
dddfff 2011-02-26 01:13:44
>Every hour, the MegaMind is allowed to call up a number of natives and ask a single question: "How many of you are truth-tellers?" or "How many of you are the liars?"

To whom does the MegaMind address this question?

For example, is the MegaMind asking just one native from among those called up to give a numerical answer concerning the whole ensemble? Or everyone assembled to give their own numerical answer concerning the whole ensemble?

The second case.
N natives are called up. M question are asked. => N*M answers are got.
zzz123
 
Rating: 72
Group: Members
2011-03-20 09:24:30
can we assume that the liars are consistent? (e.g. if there are 950 truth tellers and 50 liars, the liars will always claim that there are 950 liars and 50 truth-tellers, rather than making up random numbers on the spot)
alan
 
Rating: 231
Group: Moderators
2011-03-20 13:01:38
zzz123 2011-03-20 09:24:30
can we assume that the liars are consistent? (e.g. if there are 950 truth tellers and 50 liars, the liars will always claim that there are 950 liars and 50 truth-tellers, rather than making up random numbers on the spot)

No.
pretorik
 
Rating: 161
Group: Members
2011-04-19 10:46:42
alan 2011-02-26 09:54:01
dddfff 2011-02-26 01:13:44
>Every hour, the MegaMind is allowed to call up a number of natives and ask a single question: "How many of you are truth-tellers?" or "How many of you are the liars?"

To whom does the MegaMind address this question?

For example, is the MegaMind asking just one native from among those called up to give a numerical answer concerning the whole ensemble? Or everyone assembled to give their own numerical answer concerning the whole ensemble?

The second case.
N natives are called up. M question are asked. => N*M answers are got.
So (to be clear) In one hour I can select N natives, ask them 1 question about the group of N natives in front of me and I will receive N replies.

When you say N*M answers, presumably you mean after M hours I will have asked M x N questions?

But (presumably) N might vary as I progress my investigation?
alan
 
Rating: 231
Group: Moderators
2011-05-11 14:38:21
pretorik 2011-04-19 10:46:42
So (to be clear) In one hour I can select N natives, ask them 1 question about the group of N natives in front of me and I will receive N replies.

When you say N*M answers, presumably you mean after M hours I will have asked M x N questions?

But (presumably) N might vary as I progress my investigation?

Yes. But with one, small correction.
Yes.



 
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