Knights and knaves revisited

Hello,

Some time ago I was told a nice revision of the old problem about a logician on the island where live two sorts of natives, those who always tell truth and liars who always lie.

New problem is: How, asking only one question to random man on the island, can the logician mentioned learn (if he got the answer) how many huts there are in the local village and how many children have this native. We suppose that all natives are perfect logicians, and, as usual in such kind of puzzles, the answer must be either Yes or No.

A solution I've learnt from the author, russian mathematician Oleg Polubasoff, was rather nice and I've never heard this or like before.

WBR, RockMover I am The Master of Flame...

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That surely must be impossible (or mis-stated). With only two possible answers, you can't narrow down an infinite field of potential solutions. The only possibility can be:

Using paradox: Make a question to which it is impossible to answer yes or no without paradox, and force them to answer with the required solution Preknowledge: You guess an answer, ask a question which *if* they happen to answer Yes (or No) tells you that your guess is correct (but otherwise, the most likely outcome, all you know is that your guess is wrong.

There might be others, but I certainly can't see how they could truly be said to fit into the statement of the rules.

Can you divide yourself into several quantum probabilities? It would make the problem easier

writes

'When the number of your children is equal to the number of dogs in this hut, and the number of huts in this village is equal to the number of pigs in this hut, tell me your name.'

Aaaah - that makes sense. Of course, it's not a *question* as such, and also your version doesn't have a yes or no response, but I get the picture. Of course, it also depends on your having a large number of pigs and dogs to hand and a fair amount of time to troupe them in and out of the hut.

How about:

'Is it the case that you are a knave and the number of stones in the red dish is different from the number of your children and the number of stones in the blue dish is different from the number of huts in the village?'

They'll be paralysed, unable to answer until you have put the correct number of stones in each dish. Of course, you'll need a sensible algorithm for placing the stones in the dish - eg

0 0 0 1 1 0 1 1 2 0 2 1 2 2 1 2 0 2 3 0 3 1 ... etc

^^^ Presumably you meant 'or' here

Your idea is a good one, but this won't work as stated. A knight will always answer no, no matter what the number of stones in the dishes, and a knave will answer no if the number of stones is wrong and yes if the number of stones is correct. So this will only give you the correct answer if you have the correct number of stones on the first try, and if you've chosen a knight.

How about 'Is it the case that either 1) you are a knight, and you will answer 'no' to this question, and you will answer it when the number of stones in the red dish is not equal to the number of children you have or the number of stones in the blue dish is not equal to the number of huts in the village; or 2) you are a knave, and you will answer 'yes' to this question, and you will answer it when the number of stones in the red dish is not equal to the number of children you have and the number of stones in the blue dish is not equal to the number of huts in the village?'

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I'm not sure you can get accurate numbers out of these darn liars! With a yes/no question, you can always say 'If a woman walked up to you and asked 'bla bla bla,' what would you tell her?'

The liar would lie to the woman, so when he lies to me about what lie he would tell, his answer becomes truthful again, IF it's a yes/no answer.

But if it's not a yes/no answer, then there's trouble. I could say 'If a woman walked up to you and asked 'what is 2+2,' what would you tell her?' and he could answer '3' (since the answer by which he would lie to her would be '5'.

The same seems to go with 'If you answered with the same level of honesty that you're answering this question...'

How many IF statements are we allowed to put in these questions? How would a liar respond to something like this:

'If a woman walked up to you and asked 'what is 2+2,' based on your propensity to lie or not lie, then tell me either the one single answer that you definitely WOULD have to give her or the one single answer that you definitely WOULD NOT be able to give her.'

If this works, then we replace the 'what is 2+2,' with a statement like 'Create a single long number than consists of the number of children you have, then 20 zeroes, then the number of huts in this village.'

DOES THIS WORK:

'If a woman walked up to you and said 'Create a single long number than consists of the number of children you have, then 20 zeroes, then the number of huts in this village,' based on your propensity to lie or not lie, then tell me either the one single answer that you definitely WOULD have to give her or the one single answer that you definitely WOULD NOT be able to give her.'

Damn. You're right.

LOL - no wonder they have to be perfect logicians. It took me ten minutes to understand the question...

I think it can be simplified slightly by missing out the 'you will answer it when' part.

'Is it the case that either the number of stones in the red dish is not equal to the the number of stones in the red dish is not equal to the

A knight will be unable to answer 'no' until the correct number of stones have been placed, and a knave will be unable to answer 'yes' until then.

Cool problem. I wonder if there's a shorter solution.