Jump to content
BrainDen.com - Brain Teasers

All Activity

This stream auto-updates     

  1. Past hour
  2. Whodunit?

  3. Jelly beans join the clean plate club

    @plasmid Does the program imply a proof that it can always be done? Or is it a statement that no counterexample has yet been found? A proof could be a repeated procedure which after each application reduces the smallest number of beans on a plate. Does your algorithm always reduce the number on place C?
  4. Hats of three colors

    @ThunderCloud Nailed it. @Izzy Honorable mention
  5. Party time at Peter's and Paul's

    I think it boils down to that, but how to justify doing it?
  6. Today
  7. Born on a Wednesday

    @Izzy ... @Molly Mae ... you were halfway there!
  8. Hats of three colors

    I thinkā€¦
  9. Hats of three colors

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

    @Izzy Yes.
  11. 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
  12. 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 ...
  13. Jelly beans join the clean plate club

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

  15. Hats of three colors

  16. Born on a Wednesday

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

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

    [No content, sorry!]
  20. 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.
  21. Cubicle Stack #2

    @Thalia ...
  22. 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.
  23. Hats of three colors

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

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

    I'm very much interested. I recognize the name, too! I expect great things, my friend.
  1. Load more activity