The Gabbar Kalia puzzle – Russian Roulette July 25, 2008
Posted by ilabs in Puzzled.Tags: puzzle, trivia
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Here is an adaptation of the famous puzzle – Russian Roulette.
A scene from the movie ‘Sholay’.
‘Gabbar Singh’ (the dacoit) is furious at his accomplice ‘Kalia’. Gabbar loads his revolver with exactly two bullets in continuous slots (of the six possible slots) and points the muzzle @ Kalia’s head. Gabbar says ‘I am going to kill you’. And saying this, triggers the revolver.
But no bullet is fired. Kalia is alive and also a lot confused.
Gabbar, amused by the turn of fate, gives Kalia an option, ‘There are exactly 2 bullets in here and I am going to take only one more shot. You have a choice – 1. Either I spin the cylinder (of the revolver) again and then take a shot. 2. Or I go ahead and take another shot. Whatever now happens is your destiny. And your destiny is in your hands. What do you want me to do – Spin the cylinder and shoot OR Take another shot?’
Considering that Kalia really wants to live another day, what option should he be suggesting?
(I came across the russian roulette puzzle online. Also read in a book called ‘How would you move Mount Fuji?’ by William Poundstone. You could also read about the Russian Roulette on wikipedia http://en.wikipedia.org/wiki/Russian_roulette)
Answer
Option 2: Go ahead and take another shot.
Case 1: Revolve the cylinder again and shoot.
In this case, the no of cases where Kalia will survive is 4 (if any of the 4 empty slots gets selected again). Total no of slots is 6 (4 empty + 2 with bullet each).
Hence, Probability of Survival, P(S) = Favourable cases / Total no of cases = 4/6 = 66.66 %
Case 2: Take another shot.
In this case one empty slot has already been exhausted (as the first shot did not fire any bullet). Now to survive, the next shot must also land up on one of the remaining empty slots. Remaining empty slots = 3. Hence, favourable cases = 3.
From the total no of possible slots that can be considered, one empty slot has already been exhausted.
Also the bullets are loaded continuously. Hence, the second continuous bullet slot also has to be excluded. Because the only way that the second bullet slot can now be selected is if the first shot would have landed on the first bullet shot. But that cannot be the case, since the first shot did not fire any bullet.
Hence Total no of possible slots = 6 – 1 (empty slot that was selected for the first shot) – 1 (the second continuous bullet slot which cannot be selected) = 4
Hence, Probability of Survival, P(S) = Favourable Cases / Total Possible Cases = 3/4 = 75%
This case has a higher Probability of Survival.
Hence, Kalia must select this option.
Cool!!
By the way, I’m searching for another Gabbar-Kalia probability question. Do you know any? If you do, please mail it to me at apoorvumang@hotmail.com.
Thanks in advance!
how can u exclude the second slot? the slots are not are arranged as pairs, rather its a circular arrangement. So there could have been a bullet in the second slot and the next bullet in third slot. so if you take the possibility of survival then wouldn’t it have been 3/5, which is 60%, which is less than the first case.
I can be wrong also, please clear my doubt.
Bachu…the point is… we are trying to figure out kalia’s possibility of survival whn gabbar shoots the very next tym(which will be the final attempt on his part too). this tym if kalia survives well and good for him.
hence, we can ignore the 5th case(the case of the second bullet in the continuous slot). Coz if kalia dies this tym, gabbar saves a bullet and kalia needs to be least bothered about the second one as he must have already reached hell/heaven. so only the possibilities of survival in the most Positive way is considered by Mr.Kalia…
makes sense? or did i confuse u more?