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Posers and Puzzles

Posers and Puzzles

  1. Standard member socialist1917
    Realist
    28 Aug '05 00:49
    I am in this college class for critical thinking and spatial reasoning. I have had an easy time doing my homework this weekend until I came upon this problem. I have a vague idea of the solution, but it is probably incorrect. I was told it did have a solution.

    Congresswoman Smith open the paper and saw that a bean-counting scandal had been leaked to the press. Outraged, Smith immediately called an emergency meeting with the five other members of the Special Congressional Scandal Committee.
    Once they were all assembled in Smith's office, Smith declared, "As incredible as it sounds, I know that three of you always tell the truth. So now I'm asking all of you, who spilled the beans to the press?"
    Congressman Schlock spoke up, "It was either Wind or Pocket."
    Congressman Wind, outraged, shouted, "Neither Slie or I leaked the scandal."
    Congressman Pocket then chimed in, "Well both of you are lying!"
    This provoked Congressman Greede to say, "Actually, I know that one of them is lying and the other is telling the truth."
    Finally, Congressman Slie, with steadfast eyes, stated, "No, Greede, that is not true."
    Assuming that Congresswoman Smith's first declaration is true, can you determine who spilled the beans?

    This is from "Heart of Mathematics" by Edward B. Burger and Michael Starbird.
  2. Subscriber AThousandYoung
    It's about respect
    28 Aug '05 01:33 / 1 edit
    Originally posted by socialist1917
    I am in this college class for critical thinking and spatial reasoning. I have had an easy time doing my homework this weekend until I came upon this problem. I have a vague idea of the solution, but it is probably incorrect. I was told it did have a solution.

    Congresswoman Smith open the paper and saw that a bean-counting scandal had been leaked ...[text shortened]... ed the beans?

    This is from "Heart of Mathematics" by Edward B. Burger and Michael Starbird.
    It was Pocket.

    Wait, I'll have to think about it when I have a bit more time. I'm not sure I'm right.
  3. 28 Aug '05 04:39
    Professor Plum with the candlestick in the library.
  4. 28 Aug '05 08:12
    Originally posted by AThousandYoung
    It was Pocket.

    Wait, I'll have to think about it when I have a bit more time. I'm not sure I'm right.
    I think it is Pocket. Both Pocket and Greede are lying.
  5. 28 Aug '05 15:25 / 1 edit
    Originally posted by socialist1917
    I am in this college class for critical thinking and spatial reasoning. I have had an easy time doing my homework this weekend until I came upon this problem. I have a vague idea of the solution, but it is probably incorrect. I was told it did have a solution.

    Congresswoman Smith open the paper and saw that a bean-counting scandal had been leaked ...[text shortened]... ed the beans?

    This is from "Heart of Mathematics" by Edward B. Burger and Michael Starbird.
    Here's my analysis. Pocket's statements are inconsistent with Schlock, Wind, and Greede, so Pocket has to be lying. No one accuses Greede or Schlock of anything, so they're clear. One of them might still be a liar, but they did not spill the beans. Slie and Greede are inconsistent with each other, so one of them must be lying, that means Schlock, and Wind are truth tellers (Which makes Slie a truth teller as well). Doing a truth table on Schlock's, and Wind's statements, you can deduce that Pocket is the one who spilled the beans.
  6. Standard member ivangrice
    Deracinated
    29 Aug '05 17:55
    Originally posted by socialist1917
    I am in this college class for critical thinking and spatial reasoning. I have had an easy time doing my homework this weekend until I came upon this problem. I have a vague idea of the solution, but it is probably incorrect. I was told it did have a solution.

    Congresswoman Smith open the paper and saw that a bean-counting scandal had been leaked ...[text shortened]... ed the beans?

    This is from "Heart of Mathematics" by Edward B. Burger and Michael Starbird.
    If you know it has a solution it can hardly be impossible, can it? Pay more attention at your English class...
  7. Subscriber AThousandYoung
    It's about respect
    29 Aug '05 19:56
    Originally posted by rheymans
    Here's my analysis. Pocket's statements are inconsistent with Schlock, Wind, and Greede, so Pocket has to be lying. No one accuses Greede or Schlock of anything, so they're clear. One of them might still be a liar, but they did not spill the beans. Slie and Greede are inconsistent with each other, so one of them must be lying, that means Schlock, and ...[text shortened]... Schlock's, and Wind's statements, you can deduce that Pocket is the one who spilled the beans.
    Pocket's statements are inconsistent with Schlock, Wind, and Greede, so Pocket has to be lying.

    I am not sure how you came up with this exactly. I came to the same conclusion via this analysis:

    All of the five "other members" will be labelled with the first letter of his/her name except Slie, who will be labelled L.

    L and G are inconsistent; in fact they are opposites. One is telling a falsehood, one tells the truth. Therefore there must be two other truthtellers among the other three. If P tells the truth, this last statement cannot be true, so clearly P is false and S and W are true.

    Now, since S is true, it was either W or P. Since W is true, it's not W, so it must be P.
  8. 30 Aug '05 02:21
    Originally posted by AThousandYoung
    [b] Pocket's statements are inconsistent with Schlock, Wind, and Greede, so Pocket has to be lying.

    I am not sure how you came up with this exactly. I came to the same conclusion via this analysis:

    All of the five "other members" will be labelled with the first letter of his/her name except Slie, who will be labelled L.

    L and G are in ...[text shortened]... .

    Now, since S is true, it was either W or P. Since W is true, it's not W, so it must be P.[/b]
    Well Pocket says that both Schlock and Wind are lying, so he's definately inconsistent with them. Greede says that one of Wind, or Schlock is telling the truth, which is inconsistent with what Pocket says (He says they are both lying). So, if Pocket is telling the truth, then then we have three liars, and we know this not to be the case.
  9. 01 Sep '05 13:24 / 1 edit
    Originally posted by socialist1917
    I am in this college class for critical thinking and spatial reasoning. I have had an easy time doing my homework this weekend until I came upon this problem. I have a vague idea of the solution, but it is probably incorrect. I was told it did have a solution.

    Congresswoman Smith open the paper and saw that a bean-counting scandal had been leaked ...[text shortened]... ed the beans?

    This is from "Heart of Mathematics" by Edward B. Burger and Michael Starbird.
    This is very easy. Since Slie says the opposite of Greede, exactly one out of Grede and Slie must be lying, that leaves one liar in the other three. Since pocket claims there are two liars in the other three, pocket must by lying. That means schlock and wind are telling the truth. Hence it was EITHER Wind OR Pocket, And it was NOT Wind. Therefore it was Pocket.

    The aboce asssumes that one of them definitely leaked it. Their statements are also consistent with none of them leaking it. Perhaps it was the typist all along.
  10. 05 Sep '05 01:47
    I suppose another approach is that there are only two pieces of information about who spilt the beans -
    1) It's either Wind or Pocket
    2) It's not Wind or Slie

    For the problem to be solvable both of these statements must be true. Hence the bean spiller is Pocket.