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Everything posted by bonanova

  1. 'scuse me askin, but why has the guy been repped -1 for posting a question? And by whom? No reason I can see ... I put him back even.
  2. Place a point P at coordinates (6, 7) in a square with diagonal vertices (0, 0) and (12, 12). From P draw lines to the vertices and perpendiculars to the sides. This defines eight triangles that meet at P. Ignoring permutation of identical pieces, how many other ways can these triangles form a square?
  3. Does "greet" mean to imply "include"?
  4. Quite right. Equilateral. I changed the OP. Thanks.
  5. Place an arbitrary point P inside an isosceles equilateral triangle. From P, draw lines to the vertices and perpendiculars to the sides. Six smaller triangles now touch at P. Prove that the sums of areas of the two alternating sets of three triangles are equal.
  6. With a nod to harey and Penney and SP http://brainden.com/forum/index.php/topic/16773-a-tossing-game-you-sure-win/?p=337091 We can select a pattern of four coin tosses, say it's HTTH, and flip a fair coin until we observe it. We can determine the number of tosses on average that will precede that pattern. We call that the Wait Time. Each pattern has a wait time that may not be unique. Clearly THHT has the same wait time as HTTH. We also can select two patterns of four tosses, say TTTT and HTTT. By extension of the previous puzzle we know that HTTT is likely to happen first. Is it possible that for two 4-patterns a and b, a has the longer Wait Time but is more likely to happen first? - Puzzle due to Martin Gardner.
  7. Hi Count, and welcome to the Den. Your question solves the first part of the puzzle. To answer the second part, think of some other questions and determine what they have in common.
  8. This happens from time to time. Only one can be marked. It's your choice. Best is not always first. Sometimes "showing your work" makes for an instructive as well as a correct answer.
  9. Identical twins Cal and Hal look alike, act alike and seem to talk alike. If asked whether 2+2=5, both would say No. "Is the sky blue?" would get a Yes from them both. Yet one always tells the truth, while the other always lies. That is because the truthteller has an accurate view of the world, and truthfully presents it, while the liar has a totally inaccurate world view (he believes the sky is not blue) and wrongfully presents that view. Thus they will give the same response to the same question. Joe and Moe, themselves twins and also logicians of some repute, pondered this strange behavior one day. They wondered: if they were to meet one of the two brothers alone, would it be possible, by asking him any number of yes-no questions, to find out which one he is? Joe said, "No, it would not be possible because whatever answers you got to your questions, the other brother would have given the same answers." Moe claimed that it was possible to find out. Moe was right, and the puzzle has two parts: (1) How many questions are necessary?; and (2) more interesting yet, What was wrong with Joe's argument? - Puzzle due to R. Smullyan.
  10. somebody plz help with this doubt
  11. Extra credit: for what p(H) is this a fair game?
  12. If progress is moving forward, then what is congress?
  13. Moe: Did you hear about the actress who stabbed her boyfriend? Joe: No, I didn't. Moe: Yeah, it was, uh, Reese ... Joe: Witherspoon? Moe: No, with a knife.
  14. I thought of the lightest "cube" as three squares joined at a corner, Volume = 3a2d. The lightest "sphere" could be a "soap bubble'" Volume = pi a2d. In that sense, the "cube" could be the lighter of the two. Just a thought.
  15. What if they were made of a thin film of small thickness d?
  16. By same material I implied same density. Suppose d=1 so volume = weight. Going a bit further just for fun, which object can weigh the most, and which can weight the least?
  17. The front, side and top views of two objects give identical appearances. Object A appears in each case to be a square of side a. Object B appears in each case to be a circle of diameter a. If they are made of the same material, can you say which object is heavier?
  18. Memories of unreality, for whom Fibonacci was a favorite puzzle topic.
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