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Everything posted by bonanova

  1. bonanova

    Windows 10 -- Do you love it?

    Amid a flood of contradictory comments about how good/bad Windows 10 is, I installed it on my notebook last week, In general I like it and don't see anything buggy or undesirable. What is your experience? Thumbs up or down?
  2. bonanova

    Tiling a hexagon

    A regular hexagon is divided into 2n equilateral triangles. Pairing triangles that share an edge produces diamond shapes with three distinct orientations, as shown. Prove that any n-diamond tiling of the hexagon will use the three types in equal numbers.
  3. bonanova


    I'll give these a shot.
  4. bonanova

    Logic Puzzle with 26 Variables

    Hi Tomson, and welcome to the Den. An oldie but goodie.
  5. bonanova

    I'm not a bird

    Poe, E. Near a Raven Midnights so dreary, tired and weary. Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap -- the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor. 'This,' I whispered quietly, 'I ignore.' - Mike Keith, 1995
  6. bonanova

    Rodent Riddle

    I watch word riddles in awe from the sidelines cuz my brain is wired deductively rather than inductively. On this one, tho, as a musician of sorts, I have to say, bravo! Great riddle and great solve!
  7. bonanova

    Bowling for equilateral triangles

    OK thx.
  8. bonanova

    I might be a writer

    That's the answer I'm looking for. If you put your two posts together, you've got it.
  9. bonanova

    Brain Teaser

    Agree. If "Heidi" is the intended subject of "found," a 2nd "who" would serve no purpose except to confuse. It would not be used. Instead, Heidi is { immediately right of (Person A) } and found { more caches than (Person B) }. But since there are two "who"s, it's proper to bind them to the same (and closest) antecedent: ..... (Person A) { who has flown ... } and { who found more ... } 7) Heidi is immediately right of the person who has flown over from the States, and who found more caches than the UK cacher. 40 Traditional cache where found by a European cacher, their favourite type. Agree. They could not be Pitches 3 and 5, for example. I also fixed a typo in my interpretation post.
  10. bonanova

    Square Free

  11. bonanova

    Brain Teaser

    My interpretations I believe gives this solution
  12. bonanova

    Riddle of Lies

  13. bonanova

    Brainden races

    At the annual Brain Denizen picnic, there were the inevitable games, among them the ever-popular three-legged race. Three teams were formed by tying one contestant's right leg to another' s left leg. Fortunately all six contestants made it to the finish line without any broken bones! For purposes of this puzzle we assume all three teams ran the 100-meter course at constant speed. Team 2, comprising BMAD and Thalia, were able to beat Team 3, comprising rocdocmac and DejMar by 20 meters, but lost to the winner, Team 1, comprising plasmid and plainglazed, by 20 meters as well. By how many meters did Team 1 beat Team 3?
  14. bonanova

    I might be a writer

    Yes, sir, that is exactly the right track.
  15. bonanova

    One Girl - One Boy

    They are equally likely but they are not the same. But it's worse than that. The OP is deficient, because it does not tell us how we came to know what we know. Instead, let's create a situation where we know how we know what we know, and therefore will let us find the probability that "the other kid is a girl," unambiguously. Doing that, we know the answer is 1/3.
  16. bonanova


    So, while not being a correct solution, this would meet that qualification?
  17. bonanova


    Once letters start getting removed it quickly gets easier. At the start it's very hard. How much of a clue are you willing to share? I don't want to disclose too much, but would you be willing to confirm the politician is male and contemporaneous? Initials or country of affiliation might be too revealing.
  18. bonanova

    the distinguished matrix

    This sounds a lot, but not exactly, like eliminating variables from sets of equations. Is that the idea?
  19. bonanova

    I might be a writer

  20. 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?
  21. bonanova


  22. 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.