mmiguel

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About mmiguel

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  1. mmiguel added an answer to a question Let's meet up   

  2. mmiguel added an answer to a question Let's meet up   

  3. mmiguel added an answer to a question Let's meet up   

    i probably oversimplified this and don't have the right answer for the 3x case, but oh well - i'm tired


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  4. mmiguel added an answer to a question Let's meet up   

  5. mmiguel added an answer to a question Colored Cards   

  6. mmiguel added a question in New Logic/Math Puzzles   

    Money Bags
    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?
    • 1 reply
    • 629 views
  7. mmiguel added a question in New Logic/Math Puzzles   

    Colored Cards
    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?
    • 3 replies
    • 510 views
  8. mmiguel added an answer to a question Job Interview   


    So would I.





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  9. mmiguel added a question in New Logic/Math Puzzles   

    Job Interview
    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?
    • 5 replies
    • 2286 views
  10. mmiguel added an answer to a question Recursion   


    F(0,0) = 1
    Sorry for leaving that out.

    Nice work, you are correct!
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  11. mmiguel added a question in New Logic/Math Puzzles   

    Recursion
    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
    • 2 replies
    • 810 views
  12. mmiguel added an answer to a question I can't or I won't say   


    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".
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  13. mmiguel added an answer to a question I can't or I won't say   


    One more requirement for [A]: for finite sets, [A] = |A|
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  14. mmiguel added an answer to a question I can't or I won't say   



    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?
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  15. mmiguel added an answer to a question I can't or I won't say