At least we all agree on this

Computer Science Level 2

In a line (one in front of the other) there are $2014$ people sitting who can either lie or tell the truth and every one of them knows who lies or who tells the truth. They all say:

'There are more people who people who lie in front of me than the people who tell the truth behind me'.

How many liars are there?

The answer is 1007.

2 solutions

Adrian Neacșu
Apr 20, 2014

Think of the first one. There are no liars in front of him which means that he is a liar. Now think of the last one. In front of the last one there is at least a liar and behind him there no people who tell the truth behind him, which means that he's telling the truth. Again think if the second is lying then think if the one before the last one lies. Generalizing you will notice that the first 1007 people are liars and the rest tell the truth.

I started on the path you just described and I thought that it was just too many cases. I then just tried to generalize it and understood that was meaningless and thus I maximized it, I mean just jumped into the middle to be able to compare the bigger numbers. So, I thought of no. 1007 and 1008. I realized that for 1008 to be able to say the statement truly, the nos 1 to 1007 should be liars. Then I observed that it just fit perfectly. All the liars can lie all they want and the honest people can be honest as they want.

Shubham Agarwal - 7 years, 1 month ago

That's the part I left out of my proof.

Adrian Neacșu - 7 years, 1 month ago

I don't get it. Wouldn't it be 2013 liars and 1 person who tells the truth?

Calvin Fernandes - 7 years, 1 month ago

NO... This contradicts the whole question....

Vighnesh Raut - 7 years, 1 month ago

This question is hardly computer science.

Sharky Kesa - 7 years, 1 month ago

int i = 1; <-- number(th) of ppls int count =0;

while (i <= 2014) { int number in front = i - 1; int number_behind = 2014 -i;

if (number in front < number_behind) <-- to determine the liars { count ++; } i++; }

Lum Jian - 7 years, 1 month ago

good question

Harish Yadav - 7 years ago

There can also be case like only the first one is lying and remaining are telling truth. Y can't this be an answer??

venkatesh k - 7 years, 1 month ago

Well, the second one would have less (1) liars in front then honests (2012) behind.

Paul Paul - 6 years, 10 months ago

Abhishek Bhavsar
Apr 28, 2014

Its very simple 50% of 2014 are liars and 50% are speaking truth

Wouldn't another answer be 1 liar and 2013 who tell the truth ? Only the one in front lies and the rest of them tell the truth ?

Antonio-Gabriel Sturzu - 7 years, 1 month ago

my initial answer was 2013 because only one guy was in the front

Tasneem Khaled - 3 years, 11 months ago

At least we all agree on this

The answer is 1007.

2 solutions

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