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  1. Today
  2. Race Riddle

    Is it…
  3. Is it a factor?

    I think…
  4. Yesterday
  5. Help Bob find Alice's P(x)$%^

    Hmmm… assuming n is known to Bob, my first thoughts…
  6. The answer should be plain to see

    Lol. That's what lead to one of the other guesses. Plain to see--> crystal clear. Crystal would be fancier drinking cups though. And I couldn't quite call it white.
  7. Code to the safe

    The hard part is to generate the lock numbers from the generals, the formulas are quite complicated: There is a way to cheat: Both programs give the same list: The distribution: The solution sure is not unique, various combinations are possible. Not talking about the possibility that the lock 1 has to be unlocked to unlock locks 2 and 3.
  8. Poisoned Wine

    Yup, you both got it! I'm gonna mark Thundercloud as best answer since he was first by a couple of hours, but Aiemdao's answer is just as good and the one I had in mind (although I'm fairly sure both methods are identical).
  9. Last week
  10. Race Riddle

    Named for the first wherever you go Hundreds of cycles in column and row. Grouped into teams oft coloured the same. Hardly one in each will ever earn fame. The race will begin when ball touches ground Millions of cheers can be heard all around. You expect it to start when northern half cools, But location may often vary the rules. Too fast or too slow, not so much a race, As all are required to maintain one pace.
  11. Alice and Bob are playing the following game: Alice has a secret polynomial P(x) = a_0 + a_1 x + a_2 x^2 + … + a_n x^n, with non-negative integer coefficients a_0, a_1, …, a_n. At each turn, Bob picks an integer k and Alice tells Bob the value of P(k). Find, as a function of the degree n, the minimum number of turns Bob needs to completely determine Alice’s polynomial P(x).
  12. Is it a factor?

    Consider the set {1,11,111, …, ((10^2007) – 1)/9}. At least one of these numbers is divisible by 2007. Is the same true for 2008 (replacing 10^2007 with 10^2008, of course)?
  13. Code to the safe

    You have 7 generals and a safe with many locks. You assign the generals keys in such a way that EVERY set of four generals has enough keys between them to open ALL the locks; however, NO set of three generals is able to open ALL the locks. How many locks do you need, and list how many keys does the first general get, the second, … Is there more than one way that works?
  14. Here are the placeholders for a long division, solvable, even with none of the digits filled in. The quotient has been placed to the side. It has a decimal point, not shown, and its last nine digits are repeating. Meaning, of course, the last row of X's replicates a previous row. Can you piece together the dividend? -------------- _________________ x x x x x x / x x x x x x x ( x x x x x x x x x x x x x x x x x x ----------- x x x x x x x x x x x x x ----------- x x x x x x x x x x x x x x ------------- x x x x x x x x x x x x x ------------- x x x x x x x x x x x x x x ------------- x x x x x x x x x x x x x x ------------- x x x x x x x x x x x x x x ------------- x x x x x x x x x x x x x x ------------- x x x x x x x x x x x x ----------- x x x x x x
  15. Folding and Cutting Paper

    Looks like 21 is a bit stiff. Let's change it to 13.
  16. Dividend, please?

    =)) thanks
  17. Dividend, please?

    Here are the placeholders for a long division, along with a single digit in the quotient. Can you piece together the dividend? x 7 x x x ---------------- x x x / x x x x x x x x x x x x ------- x x x x x x ----- x x x x x x x ----------- x x x x x x x x ------- - - - - -------
  18. I want the butterscotch

    Yes, the machine only requires that one of its candies be returned it need not be one purchased with the 75 cents.
  19. Poisoned Wine

  20. Poisoned Wine

    I think…
  21. Poisoned Wine

    I heard this puzzle the other day; sorry if it's been posted before. You are the chief sommelier for a massive kingdom. The king wants to throw a banquet tomorrow, and as a result he's asked you to bring out all one thousand bottles of wine you have in the cellar. So you walk into the cellar when suddenly one of your assistants comes running up to you: "Boss! Boss! This is terrible! Someone's gone and put poison in the wine!" After calming him down a bit, you manage to squeeze some useful information out of him: There is exactly one bottle of poisoned wine. The poison is completely undetectable and fatal in any quantity. The poison takes exactly one night to work, so that the next morning anyone who drank the poisoned wine will be found dead. You rush off and tell the king. Naturally, he's very displeased: "If you can't separate that poisoned bottle from the 999 good ones, your head's gonna be on the chopping block!" You lament, "But how can I find just the one bottle by tomorrow morning without any resources?" The king relents, and tells you that he has ten criminals who have been sentenced to death. You may use them as guinea pigs to test the bottles of wine. Each criminal can test an unlimited number of bottles. How can you find the one poisoned bottle in one thousand with just ten testers? Think quickly, or perhaps the wine won't be the only thing running red tomorrow...
  22. The answer should be plain to see

    Incidentally, the title was a hint too: plain in color, and also plain -->plane, since a piece of paper is flat.
  23. I want the butterscotch

    Clarification question:
  24. There is a machine with 20 pieces of candy. Five of those candies are butterscotch. If you put in a 25 cents, one candy is provided at random. If you put in 75 cents, two candies are dropped at random but you may give the machine back one candy in exchange for a 25 cents. And if you put in $1.50 you receive 5 pieces of candy at random but are guaranteed at least one butterscotch. How much should I expect to spend to get all of the butterscotch?
  25. Coin hunt

    So if you have N coins to choose from, instead of needing log2N coins to specify its position you can guarantee that you only need (log2N / 2) + 1 flips. Nice move to halve the upper limit, but with 1000 coins you could still be in for an hour of nyan. That might work well for random configurations ... the math to figure out how many flips it would take on average would be difficult and maybe worth being its own question. But the worst case scenario if the bazillion coin is in the middle, the left half is all heads, and the right half is all tails would be a real pain.
  26. Balancing weights

    yes, but...
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