Ding! ding! Beamer vai got it right...
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Originally Posted by ZeeshanM
H#1= Choose me I am pretty and because all of them are damn liars except me!
H#2= Choose me because 3 is lying. I am an intelligent enough to grasp that.
H#3= Choose me because I am pretty and I always tell the truth like 1 is telling the lies.
H#4= Choose me because to be honest #2 is blind to the fact that she is ugly. And I don't lie...
H#5= I am ugly please don't choose me to tell you the truth because every time I lie only truth comes out!
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Assume 1 is telling the truth and the rest are all liars indeed.
That means 2 is lying, or in other words she is saying 3 is telling the truth.
But 3 says she always tells the truth. This is confirmed by 2, but let's take assumption that 1 is telling the truth then 3 is lying. And when 3 says 1 is telling lies 3 is actually saying 1 is being honest. If 4 lies then that means 2 is actually pretty as 4 lied about it.
Finally, if 1 is telling the truth that means 5 is lying, which means she is pretty, she wants you to choose her and and every time
she tells the truth, only lies come out. So far, she is the perfect candidate as she is pretty, humble, honest and intelligent. Rest, although pretty, are envious, haughty, judicious and liars .
But this whole 'proof' hinges upon the assumption that 1 is telling the truth. What happens if she is lying. That means according to her rest are not liars. So 2 is saying 3 is telling the truth. And if 3 is telling the truth (
AND confirmed by 1), that means 1 is lying., which we
did assume. If 1 is lying , that means 5 is telling the truth that she is ugly and every time she tells the truth only lies come out, which means she is pretty, humble and honest.
Either way, 5 has way better qualities than the rest. I hope someone of much higher computational abilities and mathematical minded will show a clean 'proof' of it. There
is a final rub which I haven't revealed yet.