- 28 Aug '05 00:49I 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. - 28 Aug '05 01:33 / 1 edit

It was Pocket.*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.

Wait, I'll have to think about it when I have a bit more time. I'm not sure I'm right. - 28 Aug '05 15:25 / 1 edit

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.*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. - 29 Aug '05 17:55

If you know it has a solution it can hardly be impossible, can it? Pay more attention at your English class...*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. - 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. - 30 Aug '05 02:21

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.*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] - 01 Sep '05 13:24 / 1 edit
*Originally posted by socialist1917*

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.

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.