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Everything posted by BMAD

  1. BMAD

    Poisonous apples

    There are two bowls that you and a challenger must eat from. After flipping a coin you were selected to pick the bowl that each would eat from. In the first bowl there are three out of five poisonous apples. In the second bowl, there are two out of five poisonous apples. Whoever eats from the first bowl must eat two apples at random from the bowl. Whoever eats from the second bowl must eat three random apples from the second bowl. Which bowl should you pick to eat?
  2. Imagine a piece of plywood with an array of evenly spaced nails forming small squares and consider that each square has side lengths of 1 unit. A simple closed shape is formed with a rubber band. If you knew the number of nails used in the perimeter and the perimeter itself, how could you predict how many squares can be counted inside this rubber band shape? for example say the rubber band shape is outlining these nails: * - * - * - * - * | / * * * * | / * - * - * Perimeter = 8 + 2*sqrt(2) Nails = 12 Squares: 6 squares (5 - 1x1 and 1 - 2x2) --- the result of 6, at a minimum, is what we are trying to predict.
  3. BMAD

    Squares on a plywood

    If I am not mistaken, you found a way to calculate the area every time; which is wonderful, However, I wanted to know if it could be extended to know the amount of nxn squares that were defined within the shape not the precise area.
  4. BMAD

    Squares on a plywood

    nails are 12 perimeter are the side lengths, 8+sqrt(2) Forgive my english, i think i see the confusion. When I say the number of nails in the perimeter what I am really trying to say is the number of nails throughout the shape.
  5. BMAD

    Squares on a plywood

    Hmmm, I only considered convex figures when making this problem. Let us first solve the simple case (only convex) then we could consider the more complex case with the relaxed condition.
  6. Assume we have a circle and a rectangle. The circumference of the circle is the same as the perimeter of the rectangle and the areas of each shape is also the same. Write the ratio of the circle's circumference to the diagonal of the rectangle as a function in terms of the width of the rectangle.
  7. excellent work as always bonanova but should
  8. BMAD

    Two boys

    ah, thank you.
  9. BMAD

    Two boys

    Alas, English.... But I am confused. From your interviewing you know for a fact that this family has A boy. So regardless of their birth order all we don't know is the probability that the other child is a boy. And the other child could be a boy or girl, so I still believe it is 1/2.
  10. BMAD

    Two boys

    If it is given that they already have one boy then... I get 1/2. Since the second child could either be a boy or a girl. Note: The spoiler buttons seems to be missing on mobile again.
  11. Find the limit of x^(x/2)^(x/4)^(x/8)^(x/16)^(x/32).... (a) as x goes to infinity (b) as x goes to zero
  12. BMAD

    a^b x c^a = abca

    I hope there is a nuanced way of solving this besides brute force.
  13. BMAD

    Limit of a shrinking function

    The first case
  14. BMAD

    Balancing weights

    A balance and a set of metal weights are given, with no two the same. If any pair of these weights is placed in the left pan of the balance, then it is always possible to counterbalance them with one or several of the remaining weights placed in the right pan. What is the smallest possible number of weights in the set?
  15. BMAD

    Balancing weights

    but if you place 3,4 on one side it would not be balanced.
  16. There is a machine with 20 pieces of candy. Five of those candies are butterscotch. If you put in a 25 cents, one candy is provided at random. If you put in 75 cents, two candies are dropped at random but you may give the machine back one candy in exchange for a 25 cents. And if you put in $1.50 you receive 5 pieces of candy at random but are guaranteed at least one butterscotch. How much should I expect to spend to get all of the butterscotch?
  17. BMAD

    I want the butterscotch

    To answer your second part: the machine would scan the candies and intentionally pick out a butterscotch and randomly select four candies from the remaining four. So in this case, if there is a butterscotch candy left then you are guaranteed that the first one chosen was a butterscotch.
  18. Alice and Bob are playing the following game: Alice has a secret polynomial P(x) = a_0 + a_1 x + a_2 x^2 + … + a_n x^n, with non-negative integer coefficients a_0, a_1, …, a_n. At each turn, Bob picks an integer k and Alice tells Bob the value of P(k). Find, as a function of the degree n, the minimum number of turns Bob needs to completely determine Alice’s polynomial P(x).
  19. BMAD

    Help Bob find Alice's P(x)$%^

    n is not known
  20. BMAD

    Code to the safe

    You have 7 generals and a safe with many locks. You assign the generals keys in such a way that EVERY set of four generals has enough keys between them to open ALL the locks; however, NO set of three generals is able to open ALL the locks. How many locks do you need, and list how many keys does the first general get, the second, … Is there more than one way that works?
  21. BMAD

    Is it a factor?

    Consider the set {1,11,111, …, ((10^2007) – 1)/9}. At least one of these numbers is divisible by 2007. Is the same true for 2008 (replacing 10^2007 with 10^2008, of course)?
  22. BMAD

    I want the butterscotch

    Yes, the machine only requires that one of its candies be returned it need not be one purchased with the 75 cents.
  23. BMAD

    Balancing weights

    multiples of your six seem to work too
  24. BMAD

    Balancing weights

    This contradicts the solution below. As your a > b > c > d > e > f > g solution does not follow the condition that a + b must equal the sum of the rest