BrainDen.com - Brain Teasers  # koren

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1. "Which of the two players has the advantage in this game?" My answer is Alice:
2. I suggest, we construct a kind of "triangles generator": We take a circle of any diameter, draw a chord AC from the endpoints of the chord we draw two line segments, the ends of which intersect on the circle. Symmetrically we draw two other segments on the other side of the chord and we got two triangles. When the chord is coincides with diameter the triangles are identical. The final touch – we connect the vertices of the triangles by line a-a. "Triangles generator" is ready let's start generate. For this purpose we are doing two things: 1) Moving the chord parallel to itself
3. I suggest, we construct a kind of "triangles generator": We take a circle of any diameter, draw a chord AC from the endpoints of the chord we draw two line segments, the ends of which intersect on the circle. Symmetrically we draw two other segments on the other side of the chord and we got two triangles. When the chord is coincides with diameter the triangles are identical. The final touch – we connect the vertices of the triangles by line a-a. "Triangles generator" is ready let's start generate. For this purpose we are doing two things: 1) Moving the chord parallel to itself
4. For me, it's not obvious. Imagine rain and two plots, one of which is twice larger than the other. Obviously, on a larger plot fall twice drops, i.e. probability for each drop to fall at a larger plot is approximately 0.66. And if the second plot is 1000 times larger, and if it is infinitely large? So, for me it's not obvious. And for you?
5. Depends on the technique of choice. If you choose first the point A and then B, the probability is zero, because A divides the axis on finite and infinite parts. (probability = N/infinity = 0) If you will simultaneously "throw" these points on the axis, then the odds that B is to the left or to the right from A are equal. The answer is 50-50. How you like it?
6. Look, I'm not sure in my solution too. Samething is wrong with the methodology. If we will take two arbitrary points A, B and begin to sort through all possible options by moving the third point C, we obtain an infinite number of obtuse triangles relatively a limited number of acute-angled (my solution). If we will take one arbitrary point and sort through all possibilities by moving two other points we will get completely different result. The funny thing is that according to the task conditions we have to "throw" on the plane the three points at once. (I always hated this probability stu
7. I do not know who is right-handed, etc. To my question everyone raises the right hand when they say YES. For example, a question for the left-hander: "Will you raise your right hand on the question: "2>1?"?". In normal mode, for "2>1?" he will raise his left hand, in the construction of my question he, as well as the right-hander, raises his right. Let's see how it works: 1Q to #1: "Will you raise your right hand on the question: "are you A?"?" Right hand to 1Q - the person is A 2Q tu #2: "Will you raise your right hand on the question: "are you B?"?"
8. Q really is the area between the two perpendiculars and it is really infinite but only in DIRECTION PARALLEL TO PERPENDICULARS. This direction is not relevant because the movement in this direction does not change the triangle to obtuse. The probability we are looking for depends actually on dynamics in the perpendicular direction and can be calculated by comparing two line segments outside the perpendiculars which are infinity.with the line segment Q which is tending to infinity NUMBER. So, the probability is INFINITY/NUMBER = 1. This solution is correct for one point let's say A, whic
9. The amount of gas in vessel depends on three factors - the volume of the container, the gas temperature and pressure. In our case the volume and temperature are not changing. The pressure changes. As known the air pressure decreases with increasing distance from the ground. In the first glass position the pressure therein - P1 is the average betwin Pb - bottom pressure and Pt - glass top pressure. In the second - P2 = Pb , because this is the only level of interconnected spaces. Since P2>P1 the amount of air in the second position will be more. Oh! we have not given explanation rega
10. I guess you meant to say the probability is "1" My approach is very similar to above.. but there are couple of issues you might need to address.. "since Q is also INFINITY , you can't be doing INFINITY-Q" Q is not an INFINITY but number which varies from 0 to INFINITY having a fixed value in each test point. Of course I had in mind the probability = 1. Sorry.
11. The solution I propose is based on a certain question configuration: "Will you raise your right hand on the question: (yes/no question)?" A positive response in this case - the right hand raising , the negative - left and no matter to whom you addressed the question. All the rest is not difficult.
12. Ah, ok.. I misunderstood. As you have stated, it can certainly be solved with 3 questions. Further on in the same manner...
13. In other words, you can all the time ask only one person - in terms of this exercise it makes no difference.
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