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  2. Hats of three colors

    I thinkā€¦
  3. Today
  4. Hats of three colors

  5. Party time at Peter's and Paul's

    @Izzy Yes.
  6. Hats of three colors

    @Izzy Very close. @Donald Cartmill OP restricts what each prisoner is allowed to say: Each prisoner must guess the color of his own hat, without having seen it, by saying one of the three colors
  7. Party time at Peter's and Paul's

    @Izzy As you say, the distribution is surprising. To be certain of this expected attendance at the smaller party, you might want to ...
  8. Jelly beans join the clean plate club

    I wrote a perl program to do what I said earlier...
  9. Hats of three colors

  10. Hats of three colors

  11. Born on a Wednesday

    Let's see if I remember some probability.
  12. Yesterday
  13. Emoji based math puzzle - level easy!

    5 x 20 = 100 + 14 = 114
  14. Cubicle Stack #2

    [No content, sorry!]
  15. Good-natured Trump jokes

    A joke from the internet yesterday: Trump really delivered when he said he would run the government just like his businesses. It's already shutdown! Don't worry, he still has three years to bankrupt it.
  16. Cubicle Stack #2

    @Thalia ...
  17. Digging Probabilities

    No spoiler needed: There are only three no-win-after-13-digs possibilities: BBBB BBB GGGG RR Win on dig 14 with G or R or H = 60%. Win on dig 15 with B = 40% BBBB BBBB GGG RR Win on dig 14 with R or H = 30%. Win on dig 15 with B or G = 70% BBBB BBBB GGGG R Win on dig 14 only with H = 10%. Win on dig 15 with B or G or R = 90%. Their relative occurrences were not saved in the simulations, so it's a bit uncertain how weight these cases when taking an average. But if they are equally likely, the relative dig-14 and dig-15 wins would be exactly 33.33...% and 66.66...% That is, Win 15 would be twice as likely as Win 14. For the simulations, the last few probability estimates are the least precise, because they are averages of fewer cases. In particular, the probability of going beyond 13 digs is only 5.6%, so that out of 2 million total cases, only about 112,000 14-digs or 15-digs cases were averaged. Those relative win probabilities are 35.7% and 64.3% respectively. I'll point out that the proportions of needed B G R and H (8 4 2 1) are similar to their occurring probabilities ( 40% 30% 20% 10% ). That partially justifies an equal-likelihood assumption. But the proportions do differ, somewhat. In particular, B is needed 8/15 of the time but occurs only 40/100 = 4/10 = 6/16 of the time. This fact might well make a missing-B-after-13-moves (Case 1) the most likely case of the three. That case has the highest win-14 probability. So we might expect an upward bias on the win-14 probability. The simulation suggests that is the case.
  18. Hats of three colors

    Here's a better solution.
  19. Hats of three colors

    I can save at least...
  20. I'm Back

    I'm very much interested. I recognize the name, too! I expect great things, my friend.
  21. Digging Probabilities

    Very nice! Well done!
  22. Last week
  23. Hats of three colors

    One hundred prisoners stand in a straight line seeing those visible to them only from the back. You get the picture, back guy sees 99 others, front guy sees no one. They are fitted, one each, with a hat, whose color is uniformly randomly Red, White or Blue. Each prisoner must guess the color of his own hat, without having seen it, by saying one of the three colors, and he is executed if he is wrong. The guesses are made sequentially, from the back of the line to the front. The guesses are not identified as to their accuracy, and no prisoners are executed, until all 100 guesses are made. The prisoners may collaborate on a strategy, with the object of guaranteeing as many survivors as possible. (Their communication ends, of course, once the first hat is placed.) How many can be saved, in the worst case?
  24. Digging Probabilities

    Assuming your interest is in Method 1:
  25. Born on a Wednesday

    @Molly Mae ...
  26. Cubicle Stack #2

    Only 13 this time.
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