What did the man say?

A brave explorer was once exploring a jungle in Africa when he was captured by a tribe of cannibals. The cannibals, however, were fond of problems in logic, and they said to the explorer,

"We are going to allow you to make one statement. If the statement you make is true, we will burn you alive at the stake. If the statement you make is false, then we will boil you alive in a huge pot of water."

The explorer, however, was very clever. He made a statement, and the logic-loving cannibals were forced to let him go. What statement did he make?

Suddenly he heard someone call out, "Wait!". He turned to look back and an elderly woman was standing there with her hands behind her back. She wanted to ask him one more question to really prove his cleverness. "I have some flowers behind my back, and they're yours if you know how many I have."

Her riddle was this: "All of my flowers except two are roses. All of my flowers except two are tulips. All of my flowers except two are daisies. How many flowers do I have?".

Again the explorer, such a smart man, answered correctly and went on his way, new gifts in hand. What did he say to the elderly lady?

I got both of these from this site, and I merged them together, they are not my own.

He said to the cannibals:

You will boil me in a pot of water.

This causes a paradox: they can't burn him because then his statement would be false and so they should have boiled him, and they can't boil him because then his statement would be true and so they should have burned him.

He said to the lady:

You have three flowers: one rose, one tulip, and one daisy.

Because the only solution to $(x-2)+(x-2)+(x-2)=x$ is $x=3$.

• Hmm I figured this would be quick.. I just thought it was a neat one I read Mar 4, 2017 at 19:48
• She actually has just two flowers, both carnations (or lilies or orchids or ...)
– Rubio
Mar 4, 2017 at 19:50
• @Rubio There is two possible solutions, that and the one he said Mar 4, 2017 at 19:53
• (Of course both are valid; just wanted to add that for completeness)
– Rubio
Mar 4, 2017 at 19:55
• Letting him go doesn't solve the paradox. If they let him go, his statement is false and they must boil him alive. His statement must be one that is neither true nor false if they let him go. That way, they cannot burn him, they cannot eat him alive, and releasing him does not cause a paradox. (Because if releasing him forms a paradox, burning him alive forms a paradox, and eating him forms a paradox, why should they release him?) Mar 4, 2017 at 22:17

The man said

I will be boiled alive

Because

This would cause a paradox - if he is then the statement is true which means he won't and if it is false then he will be making it true which means he wont be

• Ninja'd! :-) And I answered both parts. Mar 4, 2017 at 19:48
• @randal'thor drat didn't see your answer! (Also, I swear this is a dupe, or at least a famous paradox) Mar 4, 2017 at 19:48
• @BeastlyGerbil I think they're both pretty famous questions, I found em and liked them, felt like sharing XD Mar 4, 2017 at 19:53

The man said:

My statement is false.

Explanation:

This is a paradox: if what he said were true, the statement has to be false, controverting the assumption. Same holds if what he said were false.