A person walk into a village inhabited by 2 kind of people. First are knights. Brave, bold, and just. Knights always speak truth. Second are Knaves. They are cheats and they they always lie.
The person meets 2 men from the village, John and Bill. He wanted to know which of them is a knight and which of them is a knave. When he ask them, they replied
John: Atleast one of us is a knave.
Bill said nothing in response to John.
How can you help the person to decide who is knight and who is knave?
Answer: We will use method of contradiction. We will assume that John is a knave. This means that the statement ” Atleast one of us is knave” is false. Which means that both of them are knights. But if both of them are knight, then John is also a knight and therefore Johns statement is true. This contradicts our assumption that John is a knave. Therefore John is a knight and what he said is true. And this means that Bill must be a knave.
Final answer: John is knight and Bill is knave.
I love these problems. They are fun and are purely based on logical reasoning.
Here is another problem. You have to tell who is knight and who is knave.
John: Two of us both are knight
Bill: John is a knave
You have to tell who is who?
Answer: Answer is written below in white fonts. Drag your mouse over it to highlight and read.
Case 0: Let us assume that John is a knave ( as done in earlier problem). If John is a knave, then the statement ” Two of us both are knight” is false. Which means that either one of them is knight and other a knave, or both of them are knave.
Case 1 (both are knaves): If both of them are knaves, then Bill is also a knave. Then bill’s statement that John is a knave is a lie. This will mean that John is a knight which contradicts to our statement that both are knave. This means that this (Case 1) is incorrect.
Case 2 (either of them is knight and other is a knave): Since case 1 turns out incorrect so this case must be correct. Since we have assumed in case 0 that John is a knave, this means that Bill’s statement was true. This makes Bill a knight and John a knave*.
Final Answer: John is knave and Bill is knight.
* we cannot say that John is knight as this will contradict our assumption that john is a knave. You may ask that why can’t our assumption be wrong and John can be knight. In this case you may take exactly the opposite of what I have assumed and then work out the problem. In any case the answer will turn out to be same as I have done.