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.

Sample Problem:

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.

A simpler analysis could be:

1) Both Bill and John can’t be right as the statements are contradictory.

2) This means atleast one of them is Knave. John should be knave as he lied (both of us are Knights).

3) Since John is Knave, Bill said the truth, so Bill is a Knight.