Russian Roulette

[needimprovement]

Hi everyone,

 

This one is not very difficult, but I like it (I'm a Filipino, not a Russian )

 

Anyway, this is one of the (in)famous Microsoft's interview brain teasers that I think is actually quite good for an interview (assuming that the interviewee is expected to know the basics of logic and probability theory):

 

Interviewer suggest to play imaginary Russian Roulette with you.

 

Interviewer takes an imaginary revolver gun with 6 empty chambers, and loads 2 adjacent chambers with bullets.

 

Interviewer has the first turn: rolls the cylinder, puts it to his head, and pulls the trigger... no shot.

 

The lucky interviewer passes the gun to you and gives you two options before you put the gun to your head and pull the trigger:

 

a.) to roll the cylinder again

 

or

 

b.) not to roll the cylinder

 

Which option would you choose?

 

Bonus questions:

 

Which option would you choose if 2 bullets were placed into non-adjacent chambers?

 

Which option would you choose if it was a classic Russian Roulette - that is, if only one chamber was loaded?

Edited August 10, 2010 by needimprovement

[vordhosbn]

Either way, rolling the cylinder again is your best option - you make your chances equal.

 

There is no difference between scenario with two adjacent bullets and two separated (that is if you roll the cylinder).

[Sisyphus]

Do not roll the cylinder.

 

The interviewer clicked on one of four empty chambers. For only one of those chambers is the next chamber a bullet. Chance of survival is 3/4. However, if you spin, chance of survival is only 4/6=2/3.

 

For non-adjacent chambers, you should spin again. Two of the empty chambers have bullets after them, so chance of surviving is only 2/4=1/2, while with spinning it is still 2/3.

 

With only 1 bullet, you should also spin again. 4/5 survival vs. 5/6 with spinning.

[swansont]

Roll the cylinder. True Russian Roulette was played with large-caliber pistols (i.e. heavy bullets) that did not engage any ratchet when they were spun. The minimal friction means that the bullet would drop to the lowest point, and would never be in a position to be fired. It was a display of false bravado, not an actual gamble of your life — randomness was not part of the equation. This changes with two bullets if they are in opposite chambers, of course.

 

The answer you give to the interviewer may depend on whether s/he is actually testing probability; you might score points with the acclaimed (or dreaded) "thinking outside the box" by changing the parameters of the test, invoking history and physics instead of using probability.

[Sisyphus]

The answer you give to the interviewer may depend on whether s/he is actually testing probability; you might score points with the acclaimed (or dreaded) "thinking outside the box" by changing the parameters of the test, invoking history and physics instead of using probability.

 

Hehe. I guess the best answer would be both, depending on circumstances. If you held the gun vertically, that would make it random again. Though perhaps you would still be able to tell where the bullets are by feeling the balance. But that too could be compensated for by forcing the choice of whether to spin before you get hold the gun.

 

Of course, the real answer is that you turn the gun on the psychotic interviewer. If one of you wasn't leaving alive, then you weren't getting the job anyway.