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Everything posted by bonanova

  1. bonanova

    Brainden races

    Both answers state correctly that (a) winning distances give speed ratios and (b) combined speed ratio gives combined winning distance. What part of that can be more (or less) straightforward?
  2. bonanova


  3. bonanova

    The triangle puzzle

    You've probably seen this puzzle. There are 15 holes in triangular array. (See sketch below.) The game begins with pegs in 14 of the holes. The play is to jump pegs over adjacent pegs, removing the "jumped" pegs afterward, as in checkers. The jump is made in a straight line. To make a jump, you need a contiguous group consisting of { peg1, peg2, hole } in a straight line. Peg1 ends up in the hole, and peg2 is removed. The object is to make 13 legal jumps and end up with a single peg. This happens about 6% of the time. That is, about 94% of the time you get a configuration, with more than one peg remaining, that permits no further legal jumps. In some games the peg must end up in the original empty hole, and that happens only about 3% of the time. So, it's not a trivial puzzle. This puzzle asks for something different, and easier: Lose as badly as possible. That is, select a location for the empty hole, and then find a sequence of moves that leaves the greatest number of pegs on the board where there are no more legal jumps. It's simple enough to play, even without the game, by marking hole locations on a sheet of paper and using pennies. As already stated, there are 15 holes. There are also 36 possible jumps. For convenience in writing sequences of jumps, they can be numbered, as follows: Number the jumps like this: and the holes ---------------------------> o ------------- 1 So Jump #1 means the / \ like this: peg in hole #1 jumps 1 2 ----------> 2 3 over the peg in hole #2 into the empty 4 5 6 hole #4. o o / \ / \ 7 8 9 10 Jump #18 is peg 7 3 4 5 6 over peg 8, into 7 13 11 12 13 14 15 hole 9. / \ o-8 o 14-o Holes 4, 6, 13 / \ / \ / \ begin 4 jumps; 9 10 11 12 15 16 the others 17 19 21 23 begin two. / / \ \ o-18 o-20 22-o 24-o There are 36 jumps. 25 27 29 30 33 35 / / \ / \ \ o-26 o-28 31-o-32 34-o 36-o With symmetries taken into account, the holes have four equivalence classes: Corners (1, 11, 15) Adjacent to corners (2, 3, 7, 10, 12, 14) Edge centers (4, 6, 13) Centers (5, 8, 9) This means that there are just four distinct places for the empty hole to start a game: { 1 2 4 5 }. All other holes are symmetrically equivalent to one of these. Just to be sure the numbering above is understood, here is a winning game of the normal type. Start with pegs in every hole except #1. (The top hole is empty.) Then make these jumps: { 7 14 2 17 23 27 34 26 30 6 35 14 7 }. If done correctly, the original hole #1 contains the final peg. Enjoy.
  4. bonanova

    The triangle puzzle

  5. bonanova

    Strange math problem

    The professor writes a problem on the whiteboard, thus: 25 - 55 + (85 + 65) = ? He then inexplicably states that, even though you might disagree, the correct answer is actually 5! Explanation?
  6. bonanova


  7. bonanova

    The triangle puzzle

    Very nice! There is another solution that ends two moves earlier, leaving pegs only on the edges.
  8. bonanova

    Best words

    Have fun with this one. A bull stands in a pasture, unaware that he has just swallowed a time bomb that is due to explode in five minutes. Which word best describes the situation? Awful Abominable Dreadful Shocking Five minutes have passed, and all that's visible from the above scene is a sizable hole in the ground and scraps of bone and flesh. Which word best describes this situation? Amazing Silly Messy Noble
  9. bonanova

    Poisonous apples

    The OP does not say how many apples there are. It says the proportion that are poisonous. Question: was that the intent?
  10. bonanova


    Yes. .
  11. bonanova

    Squares on a plywood

    Doctoring the figure a bit (while I think about solving it.) o - o - o - o - o | / o o o o | / o - o - o Question: You mention the number of nails (12) and also the number of nails in the perimeter (here that's 10.) So for this example, would we be given N=12 or N=10? I'm thinking the latter, but would like to confirm.
  12. bonanova

    9-Balls Cue

    Welcome back TSLF. Nice puzzle!
  13. bonanova

    Killer quickie

  14. bonanova

    Walk the pattern

    Looks like
  15. bonanova

    Walk the pattern

    With that interpretation,
  16. bonanova

    Walk the pattern

    Assuming the above, we note that
  17. bonanova

    Walk the pattern

    Just to be clear, n = 3 4 5 7 8 9 11 12 13 ..., and CW and CCW alternate untethered (my new favorite word) to parity?
  18. bonanova

    Twins birthday puzzle

    A few years back while visiting friends, we celebrated the birthdays of their identical twin daughters Joan and Jane, born just 5 minutes apart. Joan had her party on Sunday, and Jane had hers on Wednesday. Explanation?
  19. bonanova

    Twins birthday puzzle

    Nice solve. And the "few years back" is actually two years ago, when Feb 28 was Sunday and March 2 was Wednesday.
  20. bonanova

    Random passengers

    Al and Bert are among 100 passengers assigned to one hundred seats on an airplane. Al was first to board, and Bert was last. Strangely, the first 99 passengers ignored their boarding passes and took random unoccupied seats. Bert liked the seat he was assigned and is not happy with the situation. If he's lucky, his seat is unoccupied and there's no problem. Otherwise, he insists the passenger erroneously occupying it move to his own assigned seat. The displaced passenger must then move, possibly displacing another person. This process continues until all passengers are seated. What is the probability that Al must move?
  21. bonanova

    Random passengers

    This was my take.
  22. bonanova

    Random passengers

    Nice. One thing I liked about this puzzle is that it's open to clear thinking. Even tho at first it seems too complex.
  23. bonanova

    Comparing a rectangle to a circle

    But actually ...