BrainDen.com - Brain Teasers # mmiguel

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## Everything posted by mmiguel

1. Answer for n = 2e9
2. I think I got the answer thanks to some of the other hints and ideas posted.
3. i probably oversimplified this and don't have the right answer for the 3x case, but oh well - i'm tired
4. Three bags are marked \$10, \$15, and \$20. One bag contains two \$5 dollar bills, one contains a \$5 and a \$10 bill, and one contains two \$10 bills. You are told that no bag contains the amount of money that is marked on its exterior. You are allowed to select a bag and extract a bill. How many times must you do this before before you can guarantee that you know the contents of all three bags? What is your strategy?
5. A bag contains three cards, one blue on both sides, one green on both sides, and one with one blue side and one with one green side. You pull one card from the bag and place it on the table. The side showing is blue. What is the probability that the side not showing is also blue?
6. At a job interview, your potential employer presents you with the following test: There are 2 buckets, and a bin with 50 green balls and 50 red balls. He tells you he will leave the room, and that you must place the balls in the buckets. When he comes back, he will randomly select a bucket (with equal probability), and randomly draw a ball from that bucket. If he draws a green ball, you are hired. Rules: I. No bucket can be empty II. Each of the 100 balls must be placed in one of the two buckets What do you do?
7. F(0,0) = 1 Sorry for leaving that out. Nice work, you are correct!
8. Find a closed-form expression for F(a,b) where: F(a,b) = F(a-1,b) + F(a-1,b-1), F(a,0) = 1 for all a F(0,b) = 0 for all b a and b are positive integers
9. One more requirement: If A is the real interval [0,1], and B = [0,0.5) U (0.5,1] U {2} Then [A] = B is the same as A, except that 0.5 is removed, and 2 is added. B is no longer a subset of A, but from an intuitive perspective should have the same "quantity of points".
10. One more requirement for [A]: for finite sets, [A] = |A|
11. I don't think we can say the the same about the edge with respect to the cube: The edge does not have other points than those contained in the cube. Do you agree? The subset operator would still show asymetry here. The less-than operator would not show asymmetry between the cardinalities of the two sets. Our intuition tells us, if A is a strict subset of B, then |A| < |B|. Our conclusion from this discussion is that this transformation, from a statement of sets, to a statement of cardinalities, does not hold when sets are infinite. Is there some other commonly accepted mathematical construct, e.g. denoted for set A by [A], that evaluates to a number, such that if A is a strict subset of B, then [A] < even for infinite sets?
12. sorry, thought a little more, wanted to write a little more
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