[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 380
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A 5x9 rectangle is drawn on chequered paper. There is a chip in the bottom left corner. Kolya and Sergei take turns moving it any number of cells either to the right or up. Kolya moves first. The winner is the one who puts the chip in the top right corner. Who wins if the game is played correctly?
What was the problem, Peter?
Somewhere in the middle. Did you get it right?)))
Вот еще одна вариация:
There are three gods, A, B and C, which are the gods of truth, falsehood and chance in an arbitrary order. The god of truth always tells the truth, the god of lies always deceives, the god of chance can tell both truth and lies in random order. It is required to identify the gods by asking 3 questions that can be answered 'yes' or 'no'. Each question is asked of only one god. The gods understand the language, but answer in their own language, which has 2 words "da" and "ja", and it's unknown which word stands for "yes" and which for "no".===
You can ask one god more than one question (so other gods may not be asked any questions at all).
What the next question will be and to whom it will be asked may depend on the answer to the previous question.
The god of chance answers randomly, depending on the flip of a coin hidden in his head: if the obverse falls out, he answers truthfully, if the reverse, he lies.
The god of chance answers "da" or "ja" to any question that can be answered "yes" or "no".
You should not ask questions - "paradoxes" - that can be answered with both "da" and "ja", or that cannot be answered in any way. For example, "Are you going to answer 'da' now?
That's probably up to drknn now. I'm not good at those.
Kolya, of course. The number of moves is odd in any case.
There is a solution, though.
// And it's even closer than you think... ))))
Kolya, of course. The number of moves is in any case odd.
Mathemat: Почему нечетно?
In fact, the latest "liars and honest" problems are variations on the Smillian problems (haven't you heard?)), which in turn are based on ancient Greek riddles.
Here is another variation:
There are three gods, A, B and C, which are the gods of truth, lie and chance in no particular order. The god of truth always tells the truth, the god of lies always deceives, the god of chance can tell both truth and lies in random order. It is required to identify the gods by asking 3 questions that can be answered 'yes' or 'no'. Each question is asked to one god only. The gods understand the language, but answer in their own language, which has two words "da" and "ja", and it is not known which word stands for "yes" and which for "no".
Cool puzzle, it makes your brain boil.
The beginning of the solution:
Determine what "da" and what "ja" means will not work (for 12 options you need 4 questions),
So you have to ask questions for which "da" and "ja" are unimportant.
For example:
Will you answer "da" to the question "....."? ?
the questions themselves are still being finalised.....
Let P, L, S be the gods of Truth, Lie, Chance.
1) Ask God A "Would you answer 'da' to the question 'God B is a god of chance'"?
B
C
Answer 1
П
Л
С
ja
П
С
Л
da
Л
П
С
ja
Л
С
П
da
С
П
Л
ja/da
С
Л
П
ja/da
If the answer is "ja" then ask B.
2)" Would you answer "da" to the question "god C is a god of chance "?
3)" Will you answer "da" to the question "are you the god of truth ""?
A
B
C
Answer 2
Answer 3
П
Л
С
ja
ja
Л
П
С
da
da
С
П
Л
ja
da
С
Л
П
da
ja
If the answer is "da" then ask C
2)" Will you answer "da" to the question "god B is a god of chance "?
3)" Would you answer "da" to the question "are you the god of truth ""?
A
B
C
Answer 2
Answer 3
П
С
Л
ja
ja
Л
С
П
da
da
С
П
Л
da
ja
С
Л
П
ja
da
From the answers to questions 2 and 3 it is clear who the god is.