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Everything posted by CaptainEd

  1. Jelly beans join the clean plate club

    Here’s a tiny observation about what the next to last step looks like.
  2. Waiting, again II

    much more clearly stated than my babbling. I’m tickled that I’ve shown that it can be evaluated one flip at a time, based merely on the parity of contiguous Hs. here is my argument, expressed by plagiarizing your expression: Let e be the expected number of flips from the initial (even) state There are two states that are easy to analyze and cover all the possibilities: E is the initial state, it also represents the state of having seen an even number of H (including zero), since the beginning or the most recent T. O is the odd state, representing the fact of having seen an odd contiguous run of H. State E requires e more flips. In this state, H changes to state O, while T remains in state E State O requires o more flips. In this state, H changes to state E, while T terminates with a win. That allows us to write an expression for x as the sum of these terms, weighted by their respective probabilities, all 1/2. e = 1/2{1+e} + 1/2{1+o} o = 1/2{1+e} + 1/2 substitute o into e e = 1/2{1+e} + 1/2{1+1/2{1+e} + 1/2} = 1/2{1+e} + 1/2+1/4+e/4 + 1/4 = 3/2 + 3e/4 e/4 = 3/2 e = 6
  3. Waiting, again

    Gardner sets high standard in many ways. I was a child reading Childrens Activities and a few years later I was enjoying hexaflexagons and later mathematical games. I was kneeling behind you in worship. i enjoy the puzzles here, and sometimes I don’t understand something that is obvious to anyone else. I think I may have a touch of ambiguity flu. Keep on puzzling, Bonanova!
  4. Waiting, again

    Thank you Bonanova, sorry to be so dense
  5. Waiting, again

    I want to be sure I’ve got this right. There are six (presumably distinguishable) dice. I want to demonstrate that each is capable of showing all six faces. Paul lets me roll all six (and tabulate which individual dice showed which numbers) charges $1 for the combined roll, and pays $50 when the tabulations show each die has shown all six faces. Peter has me roll one die at a time, charges $1 for the individual roll, tabulates the results, and pays $20 when each die has shown all six faces. OR... my Termination condition is seeing all six numbers on the table at once. Paul has me roll all 6 dice each time, and only pays me if I roll a full straight (123456). Peter lets me roll one die at a time, once I’ve rolled all six dice, he lets me improve my hand by rolling a single die that duplicates another one, and pays once all six numbers are showing.
  6. Hurry up and Wait

  7. Adapting a classic crossing puzzle

    Good job slashpuzzler! And neat puzzle BMAD!
  8. Two can tango

    Nice job, araver! Nice puzzle, bonanova
  9. Soldiers in a field

    Maybe this is clearer and more accurate than my previous try. Point one:
  10. Line splitting

    It's been a long time. Here's a recharacterization that recognizes a much smaller search space: Overview Definitions and additional constraint LineSplittingMValues.xlsx BonanovaSequence.xlsx
  11. Count the Flags

    Gavin, I agree, a permeable chain is necessary. Here’s a simplified (and still incomplete) proposal:
  12. Distance between nails

    Bonanova, I see your point (forehead slap echo). BMAD fooled us.
  13. Who can go the lowest?

    Thanks, BMAD, I understand now
  14. Cubicle Stack

  15. Cubicle Stack

  16. Who can go the lowest?

    I’m the only one who doesn’t know how the game works. Here are a couple of questions that may help me understand. do we all play simultaneously? Or are purchases made sequentially (so that each player is able to meet the requirement of avoiding numbers others have chosen)? Once everyone has played, how is it determined who has won? If more than person chooses a number, is that number removed, and the lowest number chosen by only one person is the determiner?
  17. How many squares?

    Kudos to both of you! Nice problem and nice solution!
  18. Move the matchstick

    Buddyboy300 has a much better answer than I did: moving the vertical stroke of the plus sign over to diagonally cross the equal sign.
  19. How many squares?

    Assuming the gray square can only touch each red square corner-to-corner or corner-to-edge, my answer is ...
  20. How many squares?

    Dang, I blew my spoiler again...I’ll be back. I’ve got an answer...sigh
  21. How many squares?

    “Touch” elucidation question: Does the gray square overlap red squares? Or can only edges overlap? Or can they only share single points?