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  1. Today
  2. Escaping the train

    Hello Charlie ..i got it wrong! I guess you are right graphically.
  3. Escaping the train

  4. Cutting yet another cake

    Good question. Not similar. Not congruent. Just equal area (viewed from top) any shape.
  5. Equal sum of numbers

    Put number 1 to 21 to the circles, so sum of the numbers in circles at each line are equal.
  6. Yesterday
  7. Same Ratio

    Except that there is one result (b=c) that you did not test:
  8. Same Ratio

    Bonanova, you are very close, your explaination is very cool, just quite not carefull. check again your exhaustive search list , you miss something.
  9. Escaping the train

    The train is travelling at 40mph. If the man can escape either way then he can cover ΒΌ the distance of the tunnel by the time the train reaches the entrance to the tunnel. If running in the other direction he will thus be half way through the tunnel by the time the train reaches the entrance. Since he only escaped by the slimmest of margins, the train effectively reaches the end of the tunnel at the same time, and hence travelled the entire length of the tunnel in the time it took the man to travel half the length of the tunnel. So the train is travelling at twice the speed of the man.
  10. Same Ratio

  11. Escaping the train

    A man walking home takes a shortcut through a train tunnel. A quarter of the way in, he hears a train whistle behind him. The tunnel is not wide enough for the man to escape being hit by the train, so he must either turn back, or go forward, at his top speed of 20 mph. Either way he will escape, but by the slimmest of margins. How fast is the train moving? All correct solutions will be accepted. The coveted bonanova Gold Star will be awarded for a solution that can be explained in words only, without equations or algebra. (e.g. without saying, "Let T be the speed of the train and D be the distance of the train from the tunnel, then t = D/T is the time that the man has in order to ..." etc. )
  12. Cutting yet another cake

    You are to cut rectangular cake into two pieces of equal size, but a rectangular piece of the cake has already been removed. Your cut must be a single straight cut. (Because the cake is frosted, a horizontal cut won't work. One piece won't have any frosting.) How would you do it? Assume the cake has constant thickness, so the problem is the same as cutting a rectangular piece of paper with a rectangular portion already removed.
  13. Same Ratio

    Sum of sides means sum of all 12 sides, sum of surface area means sum of all 6 areas. Ignore the dimensions. Let say length in m, area in m2 and volume in m3 All length are integer.
  14. Last week
  15. Same Ratio

    I'm confused about the ratios.
  16. Same Ratio

    I have a box Rasio of length, width and height of the box is a:b:c Rasio of sum of sides, sum of surface area and volume is also a:b:c find the length, width and height of the box a, b and c are integers & can be the same number.
  17. The lion and the tamer, Part 2

    @plasmid, That's an interesting conjecture - that the lion would catch the tamer iff x=0 (in your notation.) A while back, on another computer whose drive crashed, I simulated the 45-degree case (of a dog chasing a fox, I think, but that doesn't matter) and I don't think the fox was caught. I don't recall finding an angle where there was a capture. I think I'll re-write the program. It's not hard to simulate the chase, and you can get arbitrarily close to the exact solution by decreasing the time increment. ----- OK, I searched images the site has stored from previous postings. I found this one, showing a (blue) fox starting from the origin and following various radial paths. A (green) dog starts from (-1, 0) and traces the (green) pursuit paths. The figure does not seem to indicate whether there was a capture. Note this is not the original lion vs tamer situation -- the red circle is not a cage. In fact, it may have been a modified ogre-maiden situation where the red circle denotes a successful escape for the fox.
  18. I know this math problem is easy for the master here, But it will be interesting for new members I have a box, rasio of the three surface area are 1:5:10 If the volume of the box is 160m^3 find the length, width and height of the box
  19. Circles and Chords a theory

    Of course you're right. I needlessly put the chords on the same side of center.
  20. Decode a Message

    I need help decoding this message for a friend of mine - any ideas? I wanna be able to give her the answer but I'm stumped. The answer should give coordinates to a location: nXIGTvM{qODN#O5dT2fZ/3?B57lHcD]W}O<Cm9a@;7,#^7eeNo<C%w:MS5Jb9Mvb+"q]iYL5ge7w"o$MrtoA7FRtlBQcRa@G(W>ur7lH`)*ZBPg+zz`B06IU*wiY`"m]"dnX[D73=d9F`dpw_cBMfZD3tBf5<I|OiLnX(d%wTXR5$Zc7ZdPD@GUH$A;C2W<cm6dfz+gLHrpza7J`+6jtaOGZF5=vyz=d!yHN$77dT2fZ]teYF
  21. Who wants a dollar

    hmmm.... you have a point rollie.
  22. Topple Tower

    Construct the most stable 7 layered tower on a flat surface out of a double-six Domino set. The layers are made of 4 tiles (2x1x1/4") resting on their longer edges to form the squared walls. Since the pips makes the dominoes lighter..the base of the tower should have even pressure. How then tiles should be arranged or stack up?
  23. Seeking Advise from Puzzle Masters

    Hi Anthony, Do you envision having solvers come up with a single answer? That is, there is one particular virus, one particular set of <x> possible compounds, one particular value <y> for the number of slots, and therefore one particular ordered set of <y> compounds that will kill the virus? If so, then just give us values for <x> and <y> and we can work on it here. Or, will there be many instances of virii, with differing numbers for <x> and <y>, to be solved? If so, then what you need is an algorithm for generating clues. Or an algorithm for determining when a sufficient amount of random historical testing has been done to determine the 100% cure.
  24. Who wants a dollar

    That goes back to my previous path of reasoning, which briefly described the $0.01 scenario (i.e., if my friend believes I will bet 0.01, he can bet 0.02 and win everything from then on without my cooperation). It depends if my friend is trustworthy, and also whether competitive means making as much more than me as possible, maximizing their own profit, or simply guaranteeing they have funds >= to mine. It also depends whether my friends thinks that I am trustworthy, because even if he's willing to do the 0.01/0.01 trade over and over, if he thinks I'm going to betray him, he will follow the same reasoning as I had above, leading to the previously mentioned 0.50/0/50 battle.
  25. Hello! I'm designing a game that features a puzzle that is split into 12 pieces. Once you find all 12 pieces, you can begin to solve it. The inspiration for the puzzle comes from the classic board game "Mastermind", though there is probably a more technical term for this kind of puzzle. This puzzle also doesn't provide feedback about near-hits; only direct hits. Players are trying to cure a virus by looking at historical test information to deduce what combination of compounds have 100% effectiveness against the disease. There are <x> amount of compounds, and a compound is only effective if put into the right spot. Example: The final solution has Oxygen must be in slot #1, Methane must be in slot #2, .... etc. Clues to the puzzle would look something like this: Clue #1: L / O / X / M 25% Effective Clue #2: A / O / B / M 50% Effective Clue #3: A / X / B / M 25% Effective Clue #4: A / O / X / M 50% Effective Hopefully from the above information, you could deduce that A belongs in slot #1 and O belongs in slot #2. Here's my ask: I'm looking for someone far more clever than I to help design this puzzle properly. I'm concerned about how to balance it so there is only one solution, and that most (or all) of the 12 clues contribute necessary information. So that's the challenge - is anyone up for it? Thanks in advance, - Anthony
  26. Who wants a dollar

    Rollie, your friend is "logical" and "competitive". But is your friend "greedy" as well? Does your friend prefer making more money than you? or more money, period? You suggested cooperating with your friend what if you...
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