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BrainDen.com - Brain Teasers


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Everything posted by EventHorizon

  1. I wondered where I could get that extra bit... v v v v v doesn't work
  2. I've got a strategy that gets 38 (or more) on 99.8% of decks, and needs one more bit on the rest... one bit... grr. Edit: Hey... 500th post! v v v v doesn't work Edit 2: I got a strategy that guarantees 38. I'm going to flush out this idea before posting (hoping I can get 39).
  3. What things can I include in this post more than are contained in my previous posts? Notice I used more in the sense of other, extra, additional, etc. We agree, except I'm harping on the various definitions of more. Just wait until I start arguing over what the definition of is is... I've seen those examples of sets of various degrees of infinity, and have had to come up with various bijections including them. But it doesn't say whether bijections are always necessary or if math can be used instead. Perhaps in these cases the symbolic math is just shorthand for the bijections alre
  4. I've got a convex solid with a smaller volume than the one posted so far... As of yet, I'm still at a loss for the solid with the maximum volume.
  5. Yup, that's essentially what I got. What's interesting is combining the last puzzle and this one you can show that with any biased (or fair) coin you can emulate any other biased (or fair) coin or any die of any number of sides. I didn't include emulating a biased die, but that's not much of a stretch. (this does assume both heads and tails can and do occur)
  6. The golden ratio is (1+sqrt(5))/2. The reciprocal of this happens to be (sqrt(5)-1)/2 which is about .618. I happened to have a biased coin that would come up heads with exactly that probability. This was my lucky coin, and I used it to bias my decisions slightly towards the ones I favored. It was quite a tragedy when I lost this coin (not only for it's decision making qualities, but it was, coincidentally, made of gold). How can I simulate a coin toss from my missing lucky coin using a fair coin instead?
  7. Hey jim. It is common courtesy to use spoilers so others will see your answer only if they want to. Please use them in the future. (Will a mod spoilerify his post please?) That being said... good job on 1&2. I wanted a different answer for 1, but 2's answer will obviously work too. As for 3, it was a valiant attempt. You've identified a number of the needed elements in the solution, but you've missed something. Also, I think you may have misunderstood the problem as choosing between two options with an unequal probability based on N. The problem is asking you to choose from fr
  8. I took the coin from out of the biased random number generators jar that had been collecting dust in the corner of the Den, but I needed to choose between two options with 50% probability each. I thought this would be easy since I already calculated the probability that heads would come up for this coin. 1) How can I choose between the two options with 50% probability? 2) I accidently drop ujjagrawal's coin in the jar, and now don't know which one it is. I grab another coin from the jar. How can I choose between the two options with equal probability using this new coin (assum
  9. I thought of another advantage. You can easily find all the unsolved puzzles. I'm kinda interested in the puzzles that have slipped through without being answered (I've already seen a few interesting ones from my very incomplete database). I know there are a few I've forgotten about, but had an idea to try or was planning on writing code to solve. There are also some puzzles whose answers were never confirmed. Some optimization problems may have better solutions out there somewhere. Perhaps each puzzle can be tagged one of unsolved, unconfirmed, or solved. Will the search work only ba
  10. Since then I've decided that.... Though perhaps I'm reading too much into it...
  11. I'm thinking the database will simply be a condensed form of the forum. It will have the puzzles and solutions without the discussion in between. It will occasionally need to be updated with the newest posted puzzles and solutions. The more puzzles, the easier the interface and search must be. Let's keep it simple. I was thinking the interface would be fairly similar to the one I used in the simple XML editor I made. It would have a drop down box at the top that by default lists every puzzle, but you can prune the list by tag values ("tag a, but not tag b" etc). But I guess it would be
  12. Someone posted that they would like to have a paper copy of brainden to take on flights, camping, etc. I thought it would be nice to have a local electronic copy to search through, annotate, rank, mark favorites, mark ones to work on later, etc. It wouldn't be too hard to export from an electronic copy to a text document then into a word processor to format and print it out. XML is a standard, so I thought I may use that to store it. I played around with handling XML documents in java (I generally use java when I want GUIs) and worked up a simple little XML editor and started manually co
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