[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 382
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Well done, maxfade!
Solution:
Let x% of the inhabitants of the island be liars. Then (100-x)% are knights. Since each knight answered exactly one question in the affirmative, and each liar answered three questions, then (100-x)+3x=40+30+50, so x=10.
Since none of the inhabitants of the island said that they were fans of CSKA, all the liars were fans of CSKA. Each of them declared that he is a fan of Spartak, so 40%-10%=30% of the inhabitants are actually fans of Spartak.
This is not a solution - there are at least two inaccuracies here which negate the whole construct.
1. The rationale for "Every liar answered three questions" is not clear. Why exactly three? We do not know, whether it was allowed to evade the answers to some questions, or not - the condition does not say anything about it (your formulation does not say, unlike mine). But even in the case of both formulations it is not at all obvious that all the liars lied three times.
Further, the construction "Since none of the islanders said they were CSKA supporters, then all the liars are CSKA supporters" - this conclusion is not valid. Can you give a proof?
It means "each liar answered affirmatively three questions out of four asked". If the possibility of evasion is not specially mentioned in the condition, we admit the simplest variant - as in all usual problems: consider that nobody evaded anything.
2. Well, it is quite valid, provided that nobody dodged and all gave 4 answers. If there was a liar who wasn't a CSKA fan, he would have answered "yes" in the CSKA answer.
A more logically correct formulation is "Since not a single islander said that he is a CSKA fan, the whole set of liars is a subset of all CSKA fans".
It means "every liar answered affirmatively three questions out of four asked". If the possibility of evasion is not specially mentioned in the condition, we admit the simplest variant - as in all usual problems: consider that nobody evaded anything.
2. Well, it is quite valid, provided that nobody dodged and all gave 4 answers. If there was a liar who wasn't a CSKA fan, he would have answered yes in the CSKA answer.
A more logically correct formulation is "As none of the islanders said that they were CSKA supporters, the whole set of liars is a subset of all CSKA supporters".
Listen mate, I respect your knowledge potential very much. I don't want to offend you in any way. But the tone of our communication with you (sorry for being on a first-name basis - it's easier to communicate that way) is kind of flippant. You see, we perceive information differently.
No S is a P => some S is a P (No resident is a CSKA fan, therefore some residents are CSKA fans).
This construction is not even correct.
You know, please don't get mad at me, I don't know how to translate this problem into the language of formulas for logic. Neither do I know how to translate the problem I posed about finding the right door into logical formulas. If I could, I would have done it in both cases. Doubts arise when formulas produce unstable logical constructions. And only...
The challenge of love
Andrei, Boris, Kirill and Dmitri are in love with girls who are also in love with them. It turns out that none of the guys have achieved mutual love. Each of the guys loves only one girl and each of the girls only one guy. Both guys and girls are all in love with someone.Andrei is in love with a girl who is in love with a young man who is in love with Tanya. Masha is in love with a young man in love with a girl in love with Boris. Kirill is in love with the girl who loves Dima. If Boris is not in love with Zina, and the young man Galya loves is not in love with Zina, then who is in love with Andrei?
Do you want to test the stereotypicality of your perception? Solve a child's problem.
8809 = 6
7111 = 0
2172 = 0
6666 = 4
1111 = 0
3213 = 0
7662 = 2
9312 = 1
0000 = 4
2222 = 0
3333 = 0
5555 = 0
8193 = 3
8096 = 5
7777 = 0
9999 = 4
7756 = 1
6855 = 3
9881 = 5
5531 = 0
2581 = ?
Tin!!!!! You have to have a child's brain to solve this problem... No arithmetic or algebraic way to solve it :(
2
About arithmetic and algebraic ways, that's an exaggeration. We can. Write a function that extracts each digit from the number. Write a function that analyses each digit. We write a function that analyzes a set of digits.
Do you want to test the stereotypicality of your perception? Solve a child's problem.
8809 = 6
7111 = 0
2172 = 0
6666 = 4
1111 = 0
3213 = 0
7662 = 2
9312 = 1
0000 = 4
2222 = 0
3333 = 0
5555 = 0
8193 = 3
8096 = 5
7777 = 0
9999 = 4
7756 = 1
6855 = 3
9881 = 5
5531 = 0
2581 = ?
Tin!!!!! You have to have a child's brain to solve this problem... No arithmetic or algebraic way to solve it :(
I, for example, puzzled over your tables for about an hour and didn't understand anything. I think it is impossible to determine who is who in this problem. We have a random arrangement of Gods. We have six combinations in total. If we label the gods A, B and C, then the number of formations = n! = 3! = 3*2*1 = 6. You can ask all three the same question, just like in the problem I gave about finding the right door (finding the way out). The readings of the liar and the God of Truth must always coincide. Once we find this, we can say with certainty which of the two is the liar and which is the God of Truth. But there are two cases where the readings of all three gods coincide. In these cases it is impossible to say who is who. Therefore this problem has four correct solutions out of six possible ones. This suggests that the correct answer here can be given with probability 4/6=0.6(6), i.e. 66% or 67%. There is no absolute solution.
Hello, who can solve this problem?):
There is a base of different numbers. Randomly select numbers from it and formed another base (that is, there is already numbers can be repeated). You can select as many as you like, but it's a waste of resources and time.
You need to determine (probabilistically (2sigma for example)) the size of the first base from the new base.
+ It would also be nice to calculate how many samples should be made to get at least 90% of the first base.
WWer, what does "first base size" mean ? The sum of the members ?