Logic problems

I

One day, an old man called his three sons into his bedroom and told them he was close to death.

“I have decided to give you a test,” he said. “Whoever proves himself to be the wisest shall inherit my fortune.”

“Oh my God,” the eldest son said. “I had no idea you were sick.”

“Here is my test,” the old man said. “Go to the market and bring me back an item which is small enough to fit in my pocket but large enough to fill up my room. Whoever can do this will inherit my land.”

The middle son rubbed his father’s shoulder. “Dad, please, we can worry about all this stuff later. Let’s just enjoy these final moments together as a family.”

“The answer requires a leap of logic,” the father hinted.

“Dad, come on,” the eldest son said. “We’d be happy to split the money. There’s no need for this.”

“I have the solution,” the youngest son said. He was a little out of breath, because he had sprinted to the market and back.

“It’s a matchstick,” he said.

“That’s correct,” the father said. “It is small enough to fit in my pocket, but when I strike it, it fills the room with light. You are the wisest and you shall inherit my fortune.”

“What?” the eldest son said. “Dad, this is insane! How can you base such an important decision on something so trivial?”

But the father was already dead.

II

Three missionaries and three cannibals were standing on one side of a river.

“We have an interesting problem on our hands,” the first missionary said. “Our canoe only holds two passengers, and if the cannibals ever outnumber us on either side of the river, they’ll eat us. How can the three of us get across in the fewest number of trips?”

“We don’t have time for this!” the second missionary shouted frantically. “Let’s get in the canoe right now before the cannibals come at us!”

“There are only two seats,” the first missionary reminded him. “Someone can sit in the middle!”

“I bet we can solve this problem using simple logic,” the first missionary said. “For instance, we know that the first trip must involve an even number of cannibals and missionaries. Otherwise, it would create an immediate imbalance.”

“Hold on,” the third missionary said. “Are you actually suggesting that we collaborate with the cannibals?”

“Here,” the first missionary said, passing them a piece of paper. “I have figured out the solution. Let X stand for cannibal, and Y for missionary.”

1. X and Y
2. Y
3. X and X
4. X
5. Y and Y
6. X andY
7. Y and Y
8. X
9. X and X
10. X
11. X and X

“I don’t care if it works on paper,” the second missionary said. “There’s no way in hell I’m going anywhere with any goddamn cannibals.”