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harey

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Everything posted by harey

  1. harey

    100 white marbles

    The way how the marbles were selected is not known, so you cannot do better then Bonanova. However, instead of grabbing the calculator:
  2. harey

    100 white marbles

    There are 100 (quite small) marbles in a (quite large) jar. Pull out one marble, look at it, put it back. You have done it 100 times. All marbles were white. Would you bet 5:1 that they are all white? Bonus (and most interesting) question: Suppose you have 15-20 seconds to decide.
  3. harey

    Dumb robot

    Each square of an n x n grid of squares is either filled with cement blocks or left empty, such that there is at least one path from the top left corner to the bottom right corner of the grid. Outside the grid everything is filled with cement. A robot is currently located at the top left corner and wants to get to the bottom right corner, but it only knows the value of n and doesn't know the layout of the grid. It also has no method of observing its surroundings, and it is your job to give it instructions to ensure it ends up at its destination. Your instructions should be a finite list of directions (Up, Down, Left, Right) - the robot will try to move in the indicated directions in order, and, if there is a cement wall in the way at some step, it will simply fail to move in the corresponding direction and continue on with the next instruction in the list. Since the robot has no way of sensing whether it has reached its destination, it might reach the destination somewhere in the middle of your list of instructions and then later leave. The goal is to give a list of instructions, depending only on n, such that after following your instructions the robot is guaranteed to end its journey in the bottom right corner of the grid. The bad news: I do not know the solution and I cannot ask for hints.
  4. harey

    Squirrel

    A large colony of squirrels dug holes during the summer and in each hole, they put between 1 and 100 nuts (each quantity has the same probability). If each squirrel has to eat 100 nuts during the winter, how many holes must he find (in average)? Each hole contains 50.5 in average, so 2 should be enough, right?
  5. Tried to send you a private message, got an error. Tried admin@brainden, got suggestion you box is full.

  6. harey

    Squirrel

    A big step forward. Now that we found the result, it remains to find the way to find the result.
  7. harey

    3 Quickies

    @rocdocmac Pas du tout. Mais c'est ma langue maternelle, je sais même écrire.
  8. harey

    Grabbing marbles

    I see now: plainglazed's formula is the simplification of my formula I was so hard looking for. On paper, I got a kind of unreadable proof, so I fed them into my computer. Up to n=30, no difference with 6 decimals.
  9. harey

    Squirrel

    Nice try, but they do not share and they survive all. Hint:
  10. harey

    Grabbing marbles

    Though they are similar, I see at least one huge difference. In the traffic jam puzzle, you cut ANY part. In the marble problem, you cut the REMAINING part. Enough for different formulae. Remains me of http://brainden.com/forum/topic/18168-squirrel/
  11. harey

    Grabbing marbles

  12. harey

    3 Quickies

  13. harey

    Take a guess

  14. harey

    Grabbing marbles

  15. harey

    Code to the safe

    I see, I found the solution for 8 generals, confused by range() in Python. The distribution for 7 generals:
  16. harey

    Code to the safe

    The hard part is to generate the lock numbers from the generals, the formulas are quite complicated: There is a way to cheat: Both programs give the same list: The distribution: The solution sure is not unique, various combinations are possible. Not talking about the possibility that the lock 1 has to be unlocked to unlock locks 2 and 3.
  17. harey

    100 white marbles

    Hint 0: Hint 1: Hint 1.1: Hint 2: Hint 2.1:
  18. harey

    Coin hunt

    What about a hint?
  19. harey

    Dumb robot

    Congratulations, works. I checked it: I suspect a kind of recursivity, but it probably will not show up for small n. For n=2 and n=3, the robot stays where it should, which does not seem evident for larger n.
  20. harey

    Dumb robot

    I do not really understand what you mean by "simple path", but I think the answer is no. The figure H is OK, but you can very well have: * * * * * c * * * c * c c * * * c * * * * * * * * c * ... Your list must work for all these cases, as well as for all grids where there is/are one/three/four cement blocks. i.e. the solution Molly Mae proposed would not work for the first maze (so it does not matter anymore that it works for the 2nd and 3rd). Even calculating the number of possibilities for 2 blocks gives me headaches. 7 * 6 / 2? Wrong, the robot must be free to leave the corner and the lower right corner must remain accessible. To get insane...
  21. harey

    Dumb robot

  22. harey

    Dumb robot

    An interesting variant. The problem states "there is a path", but it does not state "there is a path for the robot". I think it is easier we stay with moving just to the next square.
  23. harey

    Next card is Red

    Evident after translating it to college version: Just a little bit late... I guess in a test, half an hour would be allocated for this question. I get depressed when I realize the time I needed.
  24. harey

    you are in an orgy

    The plot for all cases: Strategy I knew it would be hard, but not THAT hard.
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