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  2. Born on a Wednesday

    This is absolutely something I should have been able to reason myself into. D'oh.
  3. Building cars

    The only day where you cannot have a partial car built is the 7th day. The other days must have a whole car built to meet your quota but you can have part of a car as long as you don't make two in a given day. You must build something each shift.
  4. Building cars

    I'm not understanding something about two shifts building exactly one car. A whole car (in one shift) or two half-cars (in two shifts) seem to be the only cases. Maybe spoiler one other possibility as a means of explaining? Thanks.
  5. Jelly beans join the clean plate club

    It must be symmetric about the NW-SE diagonal, so your figure show all the cases you computed. Nice, btw. Hint
  6. Building cars

    You are in charge of building cars, you are tasked to build exactly one car a day (no more, no less) and to be clear a partial car is as good as not building a car. Your shift is separated into two parts in which you could either build a whole, half, third, fourth, or fifth of a car in a given shift. By the end of the week you are to have built 7 cars with no partial cars left over. How many ways can this be done assuming a 7-day work week?
  7. Jelly beans join the clean plate club

    The program isn't a proof, it's just an application of a greedy algorithm that starts from states with an empty plate and works backwards to see whether every state could eventually reach one with an empty plate. It covered every possible state for up to 500 jelly beans, but it doesn't prove that a plate can always be cleared if you have something like 8x1012 jelly beans.
  8. Whodunit?

  9. 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?
  10. Hats of three colors

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

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

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

    I thinkā€¦
  14. Hats of three colors

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

    @Izzy Yes.
  16. 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
  17. 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 ...
  18. Jelly beans join the clean plate club

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

  20. Hats of three colors

  21. Born on a Wednesday

    Let's see if I remember some probability.
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