This liar and truth teller riddle is one of the best brain teaser based on liar’s paradox. There is a group of liars and truth-tellers and a set of statements are given and you have to find the correct ones. The approach is to consider a statement true and validate other statements. It is usually possible to find a solution by taking up statements one-by-one and determining the truth of it’s claim. But this process can often get tedious so you can also think of shortcuts like finding contradictions and so on. Puzzles with a higher number of statements will always have these shortcuts.
100 Liar and Truth teller Riddle
You are an investigating officer and you enter a city with a total of 100 truth-tellers and liars. Your mission is to find out how many of them are truth-tellers and how many are liars.
The first one you meet says,”at least 1 of us is a liar”.
The second one says,”at least 2 of us are liars”.
The third one says,”at least 3 of us are liars”.
And so on.
The 99th one says,”at least 99 of us are liars”.
At this point you get a call from your chief and he asks,”so, how many of them are liars?”. You say,”I have no idea, chief”.
Then the 100th one meets you and says,”all of us are liars”.
You immediately call up your chief and say,”I know the answer, chief”.
Find out how which one of them are liars and which ones are truth-tellers!
The first person said that, “at least one of us is a liar”. This means that the first person is a truth-teller.
Now consider the 99th statement, “at least 99 of us are liars”. We know that the first one is not a liar. So, if his statement is true then he too is a liar. But we made assumption that his statement is true hence, his statement is a contradiction and he is a liar.
This means that the 2nd person who said that “at least 2 of us are liars” was saying the truth. So we now have 2 liars and 2 truth-tellers.
Then we consider the 98th statement and so on.
By induction, we come to the conclusion that the first 50 are truth-tellers and the last 50 are liars.
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