[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 608

 
C-4:

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.

Once again, for the "gifted": an equal result is when the numbers on the dice are the same.
 
C-4: Let there be a set A (city) equally (assumption) consisting of liars and truth-tellers.

There are no assumptions, you are making this up. There could be a million liars and not a single truth-teller in town.

It means that the"other" can be both a liar and a truth-teller and therefore equally return "Yes" or "No".

TheXpert has explained what "the other" is. That definition can be put into the judgement itself. True, it will become not so short at all.

 
sergeev:

is solved similarly as

i.e. several conditions are given via I. by Boolean algebra.


There's no way it can be solved. How can you set a logical condition using half a bit?
 
C-4: How can you set a logical condition using half a bit?
How do you understand - in your own words - the term "half bit"?
 
PapaYozh:

Once again, for the "gifted": an equal score is when the numbers on the dice are the same.

So? Who's arguing? When the numbers are equal, the money goes to the mega-brain's opponent. In other cases, it will be exactly 50-50. Now explain how the megabrain will make money on this?
 
C-4: In other cases, it will be exactly 50-50.
Why is it even 50-50?
 
Mathemat:

There are no assumptions, you are making this up. There could be a million liars and not a single truth-teller in the city.


This assumption is irrelevant because it does not determine any statistical bias (again, due to lack of information). TheExpertom's proposed solution refers to another, simpler problem, which, as far as I remember, we solved back in school in class 8.
 
Mathemat:
Why is it exactly 50-50?
Because the cubes are the same.
 
Mathemat:

TheXpert has explained what 'other' is. This definition can be entered into the judgement itself. True, it will become not so short at all.


There is no way to put it into a judgement. Conditions are formulated once and do not change towards simplification. Otherwise you get a completely different problem.
 
C-4: There's no way to make a judgement. The conditions are formulated once and not changed in the direction of simplification. Otherwise you get a completely different task.

You are making this up again: no simplification, just a clarification of the term.

I get the impression that somewhere inside the C-4 nickname sits a worm that is constantly forcing its owner to twist any phrase or task. No offence, OK?