# Brain Teaser!

Help me out please, a friend sent this to me and I can't seem to figure it out. Thanks!

"Congresswoman Smith opened the Post 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, the busiest committee on Capitol Hill.

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 Schlocke spoke up, "It was either Wind or Pocket."

Congressman Wind, outraged, shouted, "Either Slie nor 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?"

Related General Discussion News on Phys.org
Congressman Wind, outraged, shouted, "Either Slie nor I leaked the scandal."
I really hate the way that's worded, because it's unclear-- but it turns out it doesn't actually matter, since the answer is the same either way. For the record, this could be interpreted as:

1. "Either Sile did it, or it wasn't me"
2. "It was not Sile, and it was also not me"

Oh, the other thing that should be stated is that only one of them actually spilled the beans. If more than one could have done it, the problem may have other solutions.

The answer is that Pocket spilled the beans. This makes Schlocke's statement true, Wind's statement true, Pocket's statement false, Greede's statement false, and Sile's statement true.

The key here is that you know that between Greede and Sile, one of them is lying, and one is telling the truth. Hence, between the other 3 members, 2 or more of them must be telling the truth. But if Pocket's satement is true, then *BOTH* Schlocke and Wind are lying, which only results in 2 truthful statements. Therefore, Pocket must be lying, and by process of elimination (since the most false statements we can have is 2), Schlocke and Wind must be telling the truth.

Result:
Schlocke's statement is necessarily true, which means Wind or Pocket spilled the beans. But admittedly, it doesn't preclude anyone else. So Schlocke, Greede, or Sile could also have spilled the beans too.

Wind's statement is necessarily true, which means Wind did *not* spill the beans, and depending on your interpretation, Sile may or may not have spilled them.

Hence, Pocket definitely did, and Wind definitely did NOT, and it's possible that other members also spilled the beans, but we can't say for sure.

DaveE