Chapters
About Truth Tellers and Liars Logic Puzzles
Truth-tellers and liars problems which are also referred to as Knights and Knaves problems are logic puzzles in which a set of statement is given. Out of these statements, some are true and some are false. The main objective of the puzzle is to determine the statements which are true as per the given information.
The Puzzles
Example 1
(From mathsisfun.com)
You are at an unmarked intersection ... one way is the City of Lies and another way is the City of Truth.
Citizens of the City of Lies always lie.
Citizens of the City of Truth always tell the truth.
A citizen of one of those cities (you don't know which) is at the intersection. What question could you ask to them to find the way to the City of Truth?
Example 2
(From mathforum.org)
A princess visits an island inhabited by two tribes. Members of one tribe always tell the truth, and members of the other tribe always lie.
The princess comes to a fork in the road. She needs to know which road leads to the castle so as to avoid the fire-breathing dragon and rescue the prince from the wizard holding him captive in the castle. (Although the princess doesn't know it, the south road leads to the castle and the north road leads to the dragon.)
Standing at this fork in the road is a member of each tribe, but the princess can't tell which tribe each belongs to. What question should she ask to find the road to the castle?
The Trick
Don't ask about facts. If you ask about a fact, the two (liar or truth-teller) will always give opposite answers and you won't know which is which. Instead, ask about the liar or truth-teller. This will get the same answer from both a liar and a truth-teller, thereby giving you accurate information.
For example:
In version 1 above, asking where the citizen is from will get the same answer from a truth-teller and a liar.
The truth-teller would point to the City of Truth, because they're truly from there.
The Liar would also point to the City of Truth, because they're lying.
Thus, it doesn't matter which citizen you're speaking to, you know where the City of Truth is.
In version 2 above, asking the two tribesmen what the other would say will give the princess a similar result.
If she asks a truth-teller what the liar would say, the truth-teller will say: "They would tell you to go [wrong way]".
If she asks a liar what the truth-teller would say, the liar will say: "They would tell you to go [wrong way]".
Therefore, regardless of who she asks, the princess knows which way is the wrong way.
Example 3
Two men are standing in the park. One of them is wearing black shoes and the other one is wearing white joggers. The men are named John and Edward.
The guy with black shoes says "Hi! I am John"
The guy with the white joggers says "Hi! I am Edward"
If we know at least one of them lied, then which shoes John is wearing?
Trick
We will solve this example using the systematic casework. For this, we will try to have as few cases as possible.
Case 1: John is wearing black shoes and Edward is wearing white joggers. Both of these statements are true which is not possible.
Case 2: John is wearing white joggers and Edward is wearing black shoes. Both of the statements are false which is possible. Hence, John is wearing white joggers.
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Thank you, this really helped my child! He is now in Reading Boys!!!
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