[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 607
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What would the other person say if I asked him "does a city dweller have a colour television"?
The other is a liar if we ask a liar, and a liar if we ask a truthful person.
Analyzing:
If we are faced with a truth teller and a telly e, the answer is NO.
If we have a liar and a telev e in front of us, then he passes on the answer to the truth teller and twists it. NO.
If the person in front of us is truthful and the TV is not, then the liar would answer YES. Then yes.
If we have a liar and telev e in front of us, it transmits the answer of the truth teller, which is NO, and perverts it. YES.
Seems about right. But the very notion of 'other' will have to be defined in the question.
My version:
(you are a liar AND you have a telly) XOR (you are a truth-teller AND you don't have a telly). Is this correct?
Perhaps it's a little trickier. But the analysis is simpler:
Let X be the truth of the judgement "You have a telly". Then the value of the complete judgement is:
(You are a liar AND X) XOR (You are true AND not X).
For a liar, the first parenthesis is FALSE, the second parenthesis is not-X, i.e. he will answer (FALSE XOR not-X) = not-X.
For a liar, the first parenthesis is X, the second parenthesis is FALSE. Therefore the value of the judgement is (X XOR FALSE) = X. And he will answer not-X.
That would be a great solution, except for one "but". The problem states that with equal odds the money will go to the mega-brain opponent, which means he has a negative mathematical expectation in that case. You can't expect the opponent to make at least one mistake and pick a die with a lower average value - the opponent is not an idiot.
Not "at equal odds", but at "with equal numbers falling out".
Don't speculate, we're not talking about one opponent, we're talking about playing "all day long with everyone".
Alexei, show me an example of how to solve a problem with a mute.
For example, a dumb, armless right-handed person at a fork can say "woo" and "woo" but it is not known what these sounds mean, we need to find out the right way.
Alexei, show me an example of how to solve the mute problem.
For example, a dumb, armless truth-teller at a fork can say "yyyy" and "yoo", you need to know the right way.
is solved in the same way as
(You are a liar AND X) XOR (You are a truth-teller AND not X).
i.e. several conditions are given via AND. by Boolean algebra.
What would the other one say if I asked him "does a city dweller have a colour television"?
The other is a liar if we ask a liar, and a liar if we ask a truthful person.
The solution would be correct with respect to the problem of Carol Alice, where she had to ask the right way from only two dummies, one of which always told the truth, and the other always told a lie. This problem is slightly different. Its conditions say that let there be set A (the city) equally (assumption) consisting of liars and truth-telling towns people. It means that "the other" can be a liar as well as a truth-teller and therefore equally return "Yes" or "No".
It's not "at equal odds", it's "at "with equal numbers falling out".
Don't speculate, the problem is not about one opponent, it's about playing "all day long with everyone".
It is the same thing. With equal probabilities, both players have an equal chance of winning and losing. Consequently, if one of them, in this case the opponent of the megabrain, is favoured over the other, with equal results. No, the proposed method doesn't work.