Solved

problem in Island of Knights and Knaves

Posted on 2010-11-24
11
1,010 Views
Last Modified: 2012-06-21
Following problems are from the Island of Knights and Knaves, I need help in solving it.

a. Suppose you come across two of the inhabitants. You ask both of them whether the other one is a knight. Will you get the same answer in each case?
b. There are three natives A, B and C. Suppose A says ‘B and C are the same type.’ What can be inferred about the number of knights?
c. What question should you ask A to determine whether B is a knight? Justify your question using the construction given above.
d. What question should you ask A to determine whether A and B are the same type? Justify your question using the construction given above.
e. Person A says ‘If B is a knave, I am a knave.’ Determine what can be deduced about A and B.
0
Comment
Question by:hiddenpearls
  • 4
  • 3
  • 2
  • +1
11 Comments
 
LVL 84

Accepted Solution

by:
ozo earned 300 total points
ID: 34210958
a. both will give the same answer
b. odd
c. there are an infinite number of answers to this, but perhaps you are looking for "Are A and B the same type?"
d. there are an infinite number of answers to this, but perhaps you are looking for "Is B a knight?"
d. A and B are knights.
0
 
LVL 18

Expert Comment

by:deighton
ID: 34211542
c) how about asking A

'How would a knave answer if I asked him if B is a knight or a knave'?
 




0
 

Author Comment

by:hiddenpearls
ID: 34211615
@deighton
@ozo

b) c) and d)
I'm puzzled about these ..

can u please explain your answers ?
0
 
LVL 18

Expert Comment

by:deighton
ID: 34211668
my answer to c doesn't work!  if A is a knight - sorry!

0
 

Author Comment

by:hiddenpearls
ID: 34211979
@ozo can u please expalin me your answers ? I need to understand this logic
Thanks a lot
0
Find Ransomware Secrets With All-Source Analysis

Ransomware has become a major concern for organizations; its prevalence has grown due to past successes achieved by threat actors. While each ransomware variant is different, we’ve seen some common tactics and trends used among the authors of the malware.

 
LVL 18

Assisted Solution

by:deighton
deighton earned 100 total points
ID: 34213074
d) Ask A 'is B a knight?'
If A is a knight he will answer yes if B is a knight, but no if B is a knave - so yes = same type
If B is a knave he will answer Yes if B is a knave (becasuse knaves lie), he will answer no if B is a knight  -  so again 'yes'=same type

the answer you get tells you the true answer to 'are you both the same type'

e. Person A says ‘If B is a knave, I am a knave.’ Determine what can be deduced about A and B.

If A is a knight, then for the statement to be true,  B cannot be a knave, that would make the statement false

if A is a knave, then the statement is false, so B can not be a knave, because in that case the statement becomes true (B being a knave would indeed mean that A was a knave).  If A is a knave and B is a knight - the statement could still have been false, since we don't know what the implication of B being a knight is supposed to be.

there is no problem with a Knave-Knight combination

so I say that A is unknown and B is always a knight



0
 
LVL 84

Expert Comment

by:ozo
ID: 34213197
> and B is always a knight
correct.
Therefore the statement is true, and cannot be uttered by a knave.
0
 
LVL 18

Expert Comment

by:deighton
ID: 34216509
ozo - A says '‘If B is a knave, I am a knave.’'

what if it is a world where knave-knave pairs may not exist?  Then a knave could say it, but a knight couldn't say it.  B could be a knight in reality, and A could be a knave then say the statement
0
 
LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 100 total points
ID: 34219531
Problem e: A says
B is knave -> A is knave
Which is only false if B is a knave and A is a knight. Otherwise the statement is true.

Special note: If B is a knight and A is a knave the statement is TRUE it is not neutral. It is TRUE and cannot be said by a knave (this is what ozo was getting at)

From logic:
(X -> Y) = (notX or Y) so not(X->Y) = X and notY

X Y  X->Y
T T     T
T F     T
F T     F
F F     T

Open in new window


So
A             B
Knight      Knight     statement is true and A is Knight (works)
Knight      Knave     statement is false and A is Knight (does not work)
Knave      Knight     statement is true and A is a knave (does not work)
Knave      Knave     statement is true and A is a knave (does not work)

Therefore they must both be knights.

If 'knave knave pairs can't exist' then F->T is still true.
0
 
LVL 37

Expert Comment

by:TommySzalapski
ID: 34219546
hiddenpearls, when you get problems like this for most of them you can easily just set up a truth table (i.e. just look at all the possible combinations for what could happen. Even with three characters, there are only 8 possible setups) Then just look at all the possible ways it could turn out.

You can even use this type of logic to find questions to ask the knights and knaves. Just set up the 4 or 8 options and see how they would answer questions.
0
 

Author Comment

by:hiddenpearls
ID: 34469405
Thankyou so much for all of you guys ..
0

Featured Post

Highfive + Dolby Voice = No More Audio Complaints!

Poor audio quality is one of the top reasons people don’t use video conferencing. Get the crispest, clearest audio powered by Dolby Voice in every meeting. Highfive and Dolby Voice deliver the best video conferencing and audio experience for every meeting and every room.

Join & Write a Comment

Suggested Solutions

Complex Numbers are funny things.  Many people have a basic understanding of them, some a more advanced.  The confusion usually arises when that pesky i (or j for Electrical Engineers) appears and understanding the meaning of a square root of a nega…
Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
Get a first impression of how PRTG looks and learn how it works.   This video is a short introduction to PRTG, as an initial overview or as a quick start for new PRTG users.
This video shows how to remove a single email address from the Outlook 2010 Auto Suggestion memory. NOTE: For Outlook 2016 and 2013 perform the exact same steps. Open a new email: Click the New email button in Outlook. Start typing the address: …

758 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

23 Experts available now in Live!

Get 1:1 Help Now